{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " ### 一.高维高斯函数\n",
    " \n",
    " 到了结合前两节内容并编码实现的环节了，由于实际处理数据往往不是一维数据，所以需要将概率密度函数扩展到高维的情况，定义如下：   \n",
    " \n",
    " $$\n",
    " N(x\\mid u,\\Sigma)=\\frac{1}{(2\\pi)^{d/2}|\\Sigma|^{1/2}}exp[-\\frac{1}{2}(x-u)^T\\Sigma^{-1}(x-u)]\n",
    " $$\n",
    " \n",
    " 这里$u$表示均值，$\\Sigma$表示协方差矩阵，$|\\Sigma|$表示协方差矩阵的行列式，$d$表示$x$的维度，即$x\\in R^d$，类比第一节，直接写出它的对数似然函数：   \n",
    " \n",
    " $$\n",
    " L(u,\\Sigma)=log(\\prod_{i=1}^MN(x_i\\mid u,\\Sigma))=-\\frac{Md}{2}log2\\pi-\\frac{M}{2}log|\\Sigma|-\\frac{1}{2}\\sum_{i=1}^M(x_i-u)^T\\Sigma^{-1}(x_i-u)\n",
    " $$   \n",
    " \n",
    " 求最优解的思路也一样，对$u,\\Sigma$求偏导并令其为0即可：  \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " \n",
    " $$\n",
    " \\frac{\\partial L(u,\\Sigma)}{\\partial u}=\\Sigma^{-1}(\\sum_{i=1}^M(x_i-u))=0\\Rightarrow\\sum_{i=1}^M(x_i-u)=0\\Rightarrow u^*=\\frac{\\sum_{i=1}^Mx_i}{M}\n",
    " $$  \n",
    " \n",
    " $$\n",
    "  \\frac{\\partial L(u,\\Sigma)}{\\partial \\Sigma}=-\\frac{M}{2}\\frac{1}{|\\Sigma|}|\\Sigma|\\Sigma^{-1}+\\frac{1}{2}\\Sigma^{-1}\\sum_{i=1}^M[(x_i-u)(x_i-u)^T]\\Sigma^{-1}=0\\Rightarrow \\Sigma=\\frac{\\sum_{i=1}^M[(x_i-u^*)(x_i-u^*)^T]}{M}\n",
    " $$\n",
    " \n",
    " #### 补充一下上面要用到的求导公式\n",
    " （1）$f(x)=x^TAx\\Rightarrow \\frac{\\partial f(x)}{\\partial x}=Ax+A^Tx$；  \n",
    " \n",
    " （2）$f(A)=|A|\\Rightarrow \\frac{\\partial f(A)}{\\partial A}=|A|(A^{-1})^T$；  \n",
    " \n",
    " （3）$f(A)=x^TAy\\Rightarrow \\frac{\\partial f(A)}{\\partial A}=xy^T$；  \n",
    " \n",
    " （4）$f(A)=A^{-1}\\Rightarrow \\frac{\\partial f(A)}{\\partial A_{i,j}}=-A^{-1}\\frac{\\partial A}{\\partial A_{i,j}}A^{-1}$；   \n",
    " \n",
    " 由（3），（4）可推得（注意，下面的$\\Sigma$为对称阵）：   \n",
    " \n",
    " （5）$f(\\Sigma)=x^T\\Sigma^{-1}x\\Rightarrow \\frac{\\partial f(\\Sigma)}{\\partial \\Sigma_{i,j}}=-x^T\\Sigma^{-1}\\frac{\\partial \\Sigma}{\\partial \\Sigma_{i,j}}\\Sigma^{-1}x$，由于$\\frac{\\partial \\Sigma}{\\partial \\Sigma_{i,j}}$仅在位置$(i,j)$处为1，其余地方为0，所以$\\frac{\\partial f(\\Sigma)}{\\partial \\Sigma}=-\\Sigma^{-1}xx^T\\Sigma^{-1}$\n",
    "\n",
    "接下来造一些数据看看效果"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "data=np.vstack((np.random.random(size=(50,2))*0.3+[0.3,0.4],np.random.random(size=(50,2))*1.5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "u=np.mean(data,axis=0)\n",
    "sigma=np.cov(data.T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "#定义高维高斯函数\n",
    "def gaussian_nd(x,u,sigma):\n",
    "    return 1.0/(np.power(2*np.pi,x.shape[1]/2)*np.sqrt(np.linalg.det(sigma)))*np.exp(np.sum(-0.5*(x-u).dot(np.linalg.inv(sigma))*(x-u),axis=1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "#封装到utils中\n",
    "def plot_contourf(data,func,lines=3):\n",
    "    n = 256\n",
    "    x = np.linspace(data[:,0].min(), data[:,0].max(), n)\n",
    "    y = np.linspace(data[:,1].min(), data[:,1].max(), n)\n",
    "    X, Y = np.meshgrid(x,y)\n",
    "    C = plt.contour(X,Y, func(np.c_[X.reshape(-1),Y.reshape(-1)]).reshape(X.shape), lines, colors='g', linewidth=0.5)\n",
    "    plt.clabel(C, inline=True, fontsize=10)\n",
    "    plt.scatter(data[:,0],data[:,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "D:\\ProgramData\\Anaconda3\\lib\\site-packages\\matplotlib\\contour.py:960: UserWarning: The following kwargs were not used by contour: 'linewidth'\n",
      "  s)\n"
     ]
    },
    {
     "data": {
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raBd1HepS2azyU5mlocmhjG80nmxVNttvb2dInSG0r9aeZk7Niq107ovQCA07bu9g+pHpuFm50c+rHx80+YD0nHSOhx5ndd/VQG48/sbAjXjbeuc9AJ5EqVZyL/Eet+NuExQfxL3Ee3nNOx7XTnmSSsaVqGxWGXtTexpUaYCtsS3WxtZPNewwMzDDWM8YY/3/dWJ63IVJQsprtafSqMhR55ClyiJLlUWmMpP0nHTSstNIzkomOSuZREUi8Yp4YjNiufroKo/SHz3jg9bX0cfNyg0PGw9qVKqR14yjln2tMlWu4WXUdajLlje28FWbr5h5fCazT8xm6aWlzGg9g/cbvY+hnmFpmyhTAmhF3CVJqgusAroLIRJedJ0QYiX/+uQbNWpUOtlTRaCmXU0qGVfidtxtatrVpKljU27H3cYv2I+3672NQCAhEZ8Zz1+3/kKSJC5EXqC+Q316ePbAwtCixIT98IPDNHFsgoWhBRk5Gay8upK1/dbibetNw5UNaVi1Ifam9jSu2pg78XfwsvXCt4ovgTGB+Ef709q1dd7DSq1R03BlQ27F3UKpUebN4WjuiIeNBz08elDdujquVq64WrriZOFEVfOqr4WIpGWnEZEaQXhqOKHJoYQkheQ15Dj58CQZyoy8ax1MHahXuR71HXKbcTSq2ojq1tXLrLuntn1t/n7zby5HXWb64elMOTiFJReXsLDTQgbUHFBm70smfxRZ3CVJcgG2AyOEEHeLblLBKakMMQNdA3yr+OIX7EdNu5q5LdkqefIw+SFAXr/PE6EnMNQ1xMbYhl1v7aKqeVWt2/Iy9tzdQ59NfdgzdA89PHuQlpOGjqSDk4UT1sbWjGkwhkPBh2hfrT3u1u5ceXQFL1svHM0dcTBzICg+iNaurfO+/Lo6ujR1bEo3j27UssttblGjUo0yUfrA3NCcmnY1qWlX85n3hBBEpEZwK+4WN+NuEhgbyPXo6/x4/se8h1gl40o0dWpKC6cWtHRpSVPHpiW+8yoqjao24tCIQ/gF+/HJoU94Y+sbtHFtw8/dfqZe5QoZ3FYheKW4S5K0CWgH2EqSFAHMBPQBhBDLgf8DKgG//isGqvz4g7RFSTayNjMwo0HlBuy5t4eotCiqmldFoVSQoEjIXR1fWUmvGr3o5tGN+x/eL/GaIBqhQUfS4dTDU9S2r82DpAcA3E+8T03bmsRnxuNs6UzH6h1Zd30dWaosXK1cuRBxgaF1hmJnasejtEc0cWzyzNgreq8o0XspCSQpt3Wgs6UzXT265r2eo87hRuwNLkdd5mLkRc5FnGPfvX1ArlunqVNT2ru1p1P1TjRzalYmyvZKkkRXj650rN6R36/+zoyjM/Bd6cuERhP4psM3cqGycsgrQyGFEEOEEFWEEPpCCCchxO9CiOX/CjtCiHeFENZCiPr//pSYsEPJZ4h1du+MlaEVs47PAiBTmYmFoQWmBqY0c2qGZyVPTA1Mi03Yrz66yqhdo/j88OfciX/6HnUkHUKTQ7E1sWVq86n4BfuRkpWCu7U7qdmpeX7xBpUb5DWHbuvaluMPj3M34S5GekbcS7xX4b/oj3do4xqOY1WfVdyccJPETxPZM2QPk5tNJluVzdxTc2n7Z1sqLaxE3819WXF5BeEp4aVt+ivR09HjvUbvcW/SPd5v9D6/Xv4V71+82XxjM/kJrpApO5T5DNWSzhCzMrJiZruZpOWk0XBlQ/65+w+Daw0GoLlz82KZ8zGJikR+OPcD1a2qY6JvwqeHP81bnT+OQFEoFZyLOMc79d8hS5VFoiIRRwtH7E3tCYoPIj4zHkM9QxIUCUSlRVHTriZv1XqLL458gcP3DlS3ro5XpdKP0X3dsDa2pmeNnizsvJCLYy+S8GkC29/czvA6wwmICWD83vG4LHbBd4Uv35z4hpuxN19rsbQ2tuaXHr9waewlnC2dGfL3EHpt6lUmHlAy+aPMV4Vs+e3R57Zoc7Qy5sz0DkUaOzYjlmmHpjGpySQaVX16Q6JUK4nJiCnRhsiXIi8xZvcYAt4PQKVRseD0AhQqxVPhlssuLcPL1osO1TrQ6o9WPEx5yKy2s/C29Wb5leW0cGrBu77vMnLXSEbVH0Wn6p0QQhCSHIKxnjFVzKuU2P2UF4QQ3I6/zZ67e9gZtJPzEecRCGra1uTNWm8ypPYQvGxf3wemWqNmycUlzDg6A11Jl0VdFzGmwRj5wPU1pcJUhSyODDGN0LDyykq8fvFiU+CmvLIBT6Kvq1/ine7NDc1xs3IjUZGIno4eTRybEJsRy+2423nXnIs4R8+NPan1ay2UGiVOFk70rNGTli4tGd9wPEdCjlD95+o4mDrQxrUNkOuPrW5dXRb2QiJJEj52Pnza8lPOjjlL5MeRLO2xFHtTe74+8TXeS71p/FtjllxYQkLmC4PJSg1dHV0mN5tM4PuBNKzakLH/jKXXpl7PDW+VKTuU+ZU7aDdaJig+iLH/jOV02GnaubVjWc9lT2WhliZhKWHMOzWPQT6D6Fi9I3fi7/D7td9pVLURb9Z6E8iNxY9Oj6ZDtQ6oNWqarGrCxgEb81aOSYokrI2tS/M2KhRRaVFsvrGZdQHr8I/2x0DXgH7e/RjnO4721drnRVgVB4X5XmiEhl8u/sJnhz/DzMCMP/r8QW+v3sVmo0zBkdvsFRCVRsX3Z79n1vFZmOibsKjrIt6p985rtTXNUmXx3ZnvAPiq7VfEZcTx1bGvGFxrMO2rtUepVqKvq//UZ/658w/tq7UvE2GL5Z3r0df549ofrA9cT6IiEU8bTyY0nsCo+qO03j+1qE3Hb8fdZuj2ofhH+/Nhkw9Z2HnhS/MWynMP3NcNWdwLQFB8EO/sfIeLkRcZWHMgS3sszasJ87px8uFJphycwoV3L6Cno0fTVU3ZMGADFyMvkpqdyoi6IzA1MAV4bi9WmdInS5XFtlvb+PXSr5yLOIeZgRmj6o9iSrMpVLOuppU5tHEWla3KZvrh6Sy+sJiGVRqyddDW59pX1AeJTMGQxT0fCCFYemkp0w5Nw1TflKU9ljK49uBStekxGqHhZuxN6jjUeea9cf+MIyU7hStRV2jj2oblvZaTkZPxWrlb1Bo1MRkxRKZGPlVfJj4znqSsJJKzkknNTn2mcJhKo0KtyRUJSZLQlXTR09F7qmCYmYEZFoYWWBlZUcm4ErYmttib2lPZrDJVzKvkJmsZWZeJB9uVqCv8dOEnNt/YjFqoGeQziKa2Y9h2XrdIq+Bq0/fyvG+2BIR827NAY+0K2sU7O99BR9Jhw4ANdPfs/tT7xRnUIPMssri/gpj0GEbtGsX++/vp7tGd3/v8XmwHigXZsuaoc9gQsIHvzn5HcFIwDyc/pLJZ5aeuUaqVXI66jKGeIb5VfIvF5vygVCu5n3ifoPgg7ibc5V7iPR4kPSAkOeSpTlRPYqJvgo2xDZaGllgYWmBmYIaJvklebRl9HX10JV0kKbeujFqjRiVUZKuyUagUZCozSctOIzU7laSsJBIVieSoc56Zx1TfFDcrN6pZV8PDOreOjLetNz52Ptib2r92wh+ZGslPF37il4vLUKjSMVY3wVI5FEPhUahVsLYFNzgxmIF/DSQgJoB5HefxWcvP8v4NtfkgkXk1JV44rCxx5MERhm0fRkp2Cr90/4UJjScU25c9vxm0CqWC367+xndnvyMiNYK6DnX5vc/vzy3Xqq+rX+wx9f8lOSuZK1FXuProKv4x/gTEBHAn/s5TtWbsTOzwsPGguVNz3KzccLJwwsnCiSpmVXAwc8DOxE7rqftCCNJz0onNiCU6PZqotCgiUiMISwkjNCWU4MRgjoYcJVOZmfcZWxNb6jrUpUHlBvhW8aVx1cZ42HiUquA7WjiysPNCTlxuyR3lVtL0dhJtNBljdXOslMP57qBBgcR9Wlev57pKChtF5m7jztkxZxm9azSfH/mcm3E3+a33bxjpGVHVyvi5D5LXoWFFRaZCibtao2bOyTnMPjEbb1tvDo049Fy3hzZ5WQZtvwaOKJQKll9ezoIzC4jJiKGNaxt+6/0bXd27lprYPI7bPh12mrPhZzkXcY67Cf8rG+Rs4Uxdh7r08uyFj50PNe1qUqNSjVIpKStJEuaG5pgbmuNu4/7cax7XkAmKD+JW3C0CYwMJiAngl4u/kK3OBsDG2IZmTs1o5dyKNq5taOzYuFTKCsSm6GHFECxUfUjV202q3g4eGV4gLaMDkaleOFrkT+CLo864ib4JmwZuorZ9bb469hUhSSHsfGun1h8kMtqhwrhlEjITGLZ9GAeDDzKi7giW9VyWd/BYnLxoywoqPn8jmq9Pfk1UWhQdqnVgZtuZebHnJU1wYjCHHhziSMgRToSeIC4zDshdjTd3bk6Tqk1o7NgY3yq+5aY0rlKt5FbcLS5FXeJ8xHnOhp/ldnxuzoCJvgmtXVrTuXpnunl0w8fOp0Qetv91p6hJJUXvL9L192Ksr8+nLT5lWstpmOibFLstL2Prza2M2DECF0sXDg4/yPVQAzlapoSQfe5PcD36Ov229CMqLYol3Zcw1ndsia2K//tlFQgydc6SbrSWLBFJC+cWzOswj7ZubUvEnsdkq7I5HnqcPXf3sP/+foKTggFwsnCivVt72rm1o7VL61J3V5Q08ZnxnHp4iqMhRzkccpig+CAAXCxd6F2jN/28+9HWte0zIafa4kWRJ5O7WnLk0Y9svbUVF0sXfur2E329+pbq/82ZsDP03tQbQz1DDg4/SF2HuqVmS0VCFvd/2XZrG+/sfAdrI2u2D97+3IqHxcmTX9Zs6T5J+ivJ1r2Fs3kNlvb8nl41epXYFzQ9J5199/bx9+2/2XdvH+k56RjrGdOhWge6eXSji3sXPG08K5SYv4rwlHD239/P3nt7ORR8CIVKgbWRNf29+zO49mA6VOuAno52vZsvO4A/EXqCSfsnERgbSO8avfmlxy+4WJZe45tbcbfosq4LGcoM9g/bTzOnZqVmS0Whwou7EIJ5p+bx5bEvaebUjB2DdzwTdVJSrDkfwKeHphOrPoC+ZMm7dafzc9+pWheF55GjzmH/vf1svLGRf+78g0KlwN7Unr5efenr1ZcO1TqUufrkpUWmMhO/YD+2397Orju7SM1OxcHUgaF1hjKy/sgSW7mqNCp+Ov8T/3f8/5CQWNBpAe83fr9Ys11fxsPkh3Rc25GYjBj2Dd1Ha9fWpWJHRSG/4o4QolR+GjZsKIqLbFW2GLlzpGAWYtjfw4RCqSi2uV6GWqMWKy6vENbfWgu9r/XE1INTRUpWSonMfSXqivhg7wfCZoGNYBbCbqGdmLBngjgeclyo1KoSsaE8o1AqxN+3/hb9N/cX+l/rC2YhGq9sLFZdWSXSs9NLxIaQpBDRZV0XwSxEuz/biZCkkBKZ93lEpkYKryVewmSuiTgZerLU7KgIAJdFPjS23Il7alaq6Ly2s2AWYuaxmUKj0RTLPK/iZuxN0fL3loJZiLar24qbsTeLfc607DSx4vIK4bvCVzALYfiNoRi8dbDYe3evUKqVxT5/RSU+I14sPrdY1FpaSzALYTnfUnx84OMSEVuNRiNWXVklzOeZC/N55mLd9XXFPueLeJT2SHgt8RJm88zE+fDzpWZHeSe/4l6u3DKxGbH02NAD/2h/fuv9G6MajNLq+PlBpVGx8MxCZp+YjZmBGYu6LOLtem8Xqx/7QdIDllxYwh/+f5CanUod+zqMaziOYXWGvVZZq0+i1qhJy0kjLTstL0M1R52DWqjz6qDr6eihr6uPkZ7RU5mpJeHOKgxCCE6HnWbppaVsu7UNgWCQzyA+a/kZDao0KNa5Q5NDGbFjBKfDTjOi7gh+7fkrZgZmha75UtjPRaVF0WZ1GxIUCZwcebLYQ40rIhXO5x6eEk7ndZ15mPKQbYO20bNGyWfGBcUHMWLHCC5HXebNWm+ypPsS7E3ti22+CxEX+O7sd2y/vR1dHV0G+QxiYpOJNHdqXqox8nGZcdxPvE9ocigPkx8SnhpOVFoUMRkxxGbEkpCZkNcJqjCYGZg9VXKgqllVnCyc/peRauOBnYldqR4MR6RG8POFn1lxZQWp2al09+jOzLYzaerUtNjmVGlUzDk5h29OfkONSjV4v/ZSlh3veg47AAAgAElEQVTOKXDNl6LWiglNDqXVH61QCzVnR5/VWr0cmVwqlLiHJIXQYW0HEhW5rdBK+kBHCMGyy8uY6jcVU31TlvVcxqBag4ptruOhx/nm5DccCz2GlZEV7zd6n4lNJpZ4I+5ERSLXHl3jesx1AmMDuRV3i6D4IFKzU5+6zsbYhqrmValiVgU7UzsqGVfKK0Hw3/IDupIuOpIOAoFKo0KpVpKtziYjJ4O0nDRSslJIzkomXhGfl5UamRpJguLpOulWRlbUtK1Jbfvaedmo9SvXL5HchidJyUph6aWlLDq3iARFAj09ezK3w9xibUx9LOQYb/39FvEZqdhkT8ZU0+qp919VgkAbpQtuxt6k9erW2Jvac3bM2edmWssUDq2JuyRJfwC9gFghRO3nvC8BPwE9gExgpBDi6qsm1pa4BycG025NOzKVmRwcfvCZjknFTUJmAqN3j2b3nd108+jG6r6riy0q50ToCb469hWnwk5RxawKU5tPZVzDcZgbmhfLfE+i0qi4Hn2dM+FnOBdxjgsRFwhJDsl738HUAR87H3zsfKhRqQbu1u5Us66Gq6VriQhqpjKTh8kPeZD0IK/eze342wTGBpKoSARye8zWtq9Nc6fmtHJpRVvXtjhbOhe7bZAbhrrkwhIWnl1ISlYKI+qNYG6HucXW8CUyNRL3HzqSrXMHS+UQLFVDkcjdybyq5ou2asWceniKTus60dypOX4j/MpEI/GygDbFvQ2QDqx9gbj3ACaRK+5NgZ+EEK/ce2pD3EOSQmjzZxsUSgVH3j5SrKuh53E+4jxvbn2T6PRoFnZeyEdNPyoWV4B/tD+fHf4Mv2A/qppX5fNWn/Ou77vF1oQbcncIt+Ju4Rfsx5GQI5wKO5W3Ine2cKaJYxMaV83NWK1fuT52pnbFZktREEIQmRbJ1UdXuRx1mfMR57kQeSHvXtyt3elcvTNdPbrSsVrHYn9QJimS+Pb0t/x04Sd0JB2mt5rOpy0/LZb/y+bzDxCY+QMZeocxUbXBVjkZCYMSWbk/ZkPABobvGM5Y37Gs6LVCzqHQAlp1y0iS5AbseYG4rwCOCyE2/fv3O0A7IcSjl42pDXFPVCQy5O8hLOi0gPqV6z/3muJoIvDYDTP5wGScLJz4a9BfxbJjiEyN5IujX7Du+jqsja35otUXTGg8odji0rNV2RwLPcauoF3svbeX8NTcZsmeNp50qNaBtq5taeXSqsRWu8WFWqMmMDaQ46HHORpylGOhx0jPScdA14D2bu3p792f/jX7F+t5SWhyKNMOTWPbrW1Ut67Orz1+patHV63OsfNaJNO3BxAjtpCsvwZDdW1cxEwWDmherD73/zLjyAzmnZ7H0h5LmdB4QqHuReZ/lKS47wG+FUKc/vfvR4DPhBAvVe6SyFAtjiYC2aps3t/7Pqv9V9PTsyfr+q/TekRKtiqbRecWMffUXJQaJR81/YgvWn+BlZGVVueB3CSng/cPsuXmFv65+w+p2amY6pvSxb0L3T2608W9C65Wrlqf93UiR53D2fCzeQ2ug5OC0ZF06FCtA8PqDGNgzYHFtqI/8uAIE/ZN4G7CXYbXHc7iroupZFJJa+M/XtzcTTtAgsGPuFp4cn7ssVc2o9HmokgjNPTZ1Ae/YD9OjjopZ7EWkZIU973A/P+I+6dCiCvPuXYcMA7AxcWl4cOHD185d1HQdk3r2IxY+m/pz9nws3zV5itmtZul9azAJ7/s/b37832X76luXV2rcwghuBR1iT/9/2TLzS0kKhKxNrKmn3c/BtYcSMfqHYvV5fM6I4QgMDaQrTe3svHGRh4kPcBE34Q3a73JON9xNHNqpnXXQpYqi3mn5jH/9HwqGVdiVZ9V9KrRS6tzAPgF+9F/S3+cLJw4+vbRfFeYfB4FFf8kRRINVzZEpVHhP95fPmAtAhXCLfMqtNlEICg+iB4bevAo/RFr+63VejRMoiKRjw9+zJrra3C3dmdpj6Va36anZqey7vo6Vl5dSUBMAEZ6RvT37s/wusPpXL1zsRXDKqsIITgXcY7V11az+eZm0nPSqV+5Ph82+ZChdYa+tKdoYfCP9uedne8QEBPA+IbjWdR1kdZdcGfCztB9Q3fsTe05PvJ4oQ50C7sjvhx1mRa/t6BnjZ5sf3O77H8vJPkVd20sO3cDb0u5NANSXiXsJcWLmgUUtInA2fCztPyjJRnKDE6MPKF1Yd9zdw+1fq3FhsANfN7qcwLfD9SqsN9LuMfEfRNxXOTIxP0T0dfRZ3nP5URPjWbjwI308OwhC/tzkCSJFs4t+K3Pbzya+ojlPZej0qgYvXs0rotdmX9qPilZhY/X/y/1K9fn4rsX+aT5Jyy/spwmq5pwJ/6O1sYHaOnSEr8RfsRmxObWg0mPKfAYL+tR8DIaVW3E/I7z2Rm0k9+v/V7geWUKRn6iZTYB7QBbIAaYCegDCCGW/xsK+QvQjdxQyFGv8rdD2fG577u3jzf+egMnCycODD+gVRdJek46Uw5MYdW1VdR1qMuafmteeDD8JJnKTNQa9Sv9wJciLzH/dO6XSV9Xn7dqv8XExhNp7NhYW7dQ4RBCcCTkCN+d/Q6/YD+sjKyY0mwKk5tN1mqzkoP3DzJ8x3CyVFms6beGATUHaG1syF3Bd1mfWwX0+MjjBTrPKcqOWCM0dF7XmYuRFwl8PxA3K7cC2S1TwZKYXkZRDoa23tzK0O1DqetQl/3D9ms1euLao2sM3jaY+4n3+azlZ8xuPztfccB+wX58e/pbDPUMGVlvJA2rNsTDxuO51w7eNhi/YD8+aPwBk5pMeukh2pc7A9l0IRy1EOhKEkOaOjOnX9FSxxVKRV5P1YfJD4lMi+RR+qO8LNXHTbIzlZkoVAqUaiWC/5UeMNA1wFjPGDMDM6yMrLAxtsHO1A4HUwcczR1xsXTBzcoNDxsPbE1sS3ybf/XRVb4+8TW77uyiknElZrSewQdNPtBaPHdEagQD/xrIxciLzGw7k5ltZ2r1Hv2C/ei1sRctnFtwcPjBfLuZinqW9TD5IXWW1aGJYxMOjTgku2cKiCzuRWRj4EZG7BhBc6fm7B26F0sjS62MK4RgxZUVfHTgI+xM7NgwYEO+G3XEZcTRfUN3FnZeSKYyk1MPT5GlymJik4l4VvLMLRb0xBflUdojzAzMXrnC/3JnIOvPhz3z+vBmLvkSeCEEwUnBXI66jH+0P4GxgdyMvUlYSlieWEOuYDuYOuBg5oCtiS1WRlaYG5hjqm+KkZ4R+rq5zbEfZ6fmqHPIVGaSnpNOSnYKiYrEvKzU52XB+tj5UNe+Lg2qNKBR1UbUtq9dInVorkRd4fMjn3PowSHcrd1Z1HURvWv01opoZauyeW/Pe6y5voYhtYewuu9qrfr6NwZuZNj2YQyrM4x1/dfly2Zt7IiXX16eG3XWdzUj648srPkVElnci8CWG1sYun0orV1as2foHswMzLQyrkKpYPze8ay9vpbuHt1Z239tgVrWBScG887Odzg9+jSQ22Fq151dpOekM6P1jEI/gNw/34f6Ob8HupJE8Pwez7yu0qi4EnWFY6HHOB12mnMR5/KyQPV19PG29aa2fW28bb3xsPGgunV1XC1dcTBz0Fp0UVp2GuGp4TxIesC9hHsExQdxM+4mATEBpOWkAbmt8po5NaONSxs6Vu9IU8emxXq2cOD+AT4++DG342/T07Mnv/T4RStuByEEC84s4PMjn9POrR273tqlVRfQ3JNz+fLYl8ztMJcvWn+Rr88UNVRSIzS0Wd2GoPgg7k66K0fPFABZ3AvJ7ju7GbBlAC2cW7B/2H6tpc5HpUXRb3M/LkVdYlbbWXzV9qt8C12WKisvNHHQ1kHUta/LV22/AnIPe3cG7aSHZw/aubUrlG1u0/e+8L3Qf32o0enR7Lm7h3339nEk5Ejeytnb1puWzi1p6tiUxo6N8bHzKdU0c43QEJyYu4s4F3GO02Gn8Y/2RyCwMLSgc/XO9K7Rm95evYtFUJRqJUsuLuH/jv0fAPM7zueDJh9o5aG2PmA9o3aNop5DPQ4OP6i1eHghBMN3DGdT4Cb2DN1DD89nH+jFQWBMIA1WNGBcw3H82vPXEpmzPCCLeyE4Hnqcbuu7Ua9yPQ6POKy1xBX/aH96buxJanYq6/uvp69333x9LiotioF/DcTd2h0jPSMWd1vMpchLbLqxiS7uXXjD5w3UGjUT903EycKJGW1mFMq+F63chZTIlL4JbLu1jbPhZxEInC2c6ebRjU7VO9HOrV2xZnFqiyRFEsdCj3Hg/gH23ttLVFoUejp6dK7emWF1htHPu5/W69+EpYQxfs949t/fT3u39qzpt0Yrmb177+5l4F8D8bL14sjbR7TWrFyhVNDijxY8TH7ItfeulVji2of7P2TppaVcH3+d2vbPRFrLPAdZ3AtIYEwgrVa3wtHckVOjTj2zKirsNvTwg8P039IfKyMr9gzZk+/6N5nKTMb+M5YGlRvwXsP3eHvn29Sxr0M7t3ZEpkbi98CPQT6D6OPVh9+u/Ma9xHvM7zgfXR3dAt/7kz53Ddlk6p4lQ/cIWbrXAUE9h3oMrDmQvt59qWNfp0wfgD1O4Pr71t9submFhykPMTMwY2jtoYxvNF6rddeFEPxx7Q8+OvARBroGrO67Ot8P9pdx+MFhem/qjbetN0ffPqq1DOn7iffxXeFLbfvanBx1skTOKxIyE/BY4kFzp+bsG7av2OcrD1ToNnsFJTI1UjgtchJVf6gqwpLDnnl/x9UI4f3lfuH62Z68H+8v94sdVyNeOu5fN/4S+l/rizq/1hERKS+/9r/kqHJEl3VdhN99PyGEELHpsWLSvkniuzPfiatRV8XWm1uF0yInMW73OFFpQSVxLvxcgcb/LxM27xWWX/YXOjPNBLMQVvMcxVdHvxJBcUFFGvd1Rq1RixOhJ8TInSOF8RxjwSxEy99bir9v/S3UGrXW5rmXcC+vO9anfp9qpc3hgXsHhME3BqL5quYiIydDC1bmsilwk2AWYtaxWVob81UsPL1QMAtxIvREic1ZlqEidmIqDAqlgrZ/tuVW3C1Ojz793DjzwoR+rfFfw+jdo2nu1Jw9Q/fkO444PCUcQz1D7E3tWXx+MUq1kpH1R2JnasetuFvMPjGb4XWG09urN4ExgaRkp+Bm5Vbo0rHnws+x8OxCdgXtQldHlwE1BzDOdxztq7UvtYbLpUFyVjJ/+v/Jzxd+JiQ5BK9KXnzZ5kuG1B5SqN3Qf8lWZTP5wGSWX1lOV/eubHljS5EjsP6+9TeDtg6it1dvtr+5/YV2FnTXOWLHCDYFbuLi2Iv4VvEtko35QaFU4P6zO56VPDkx8kSxz1fWKckM1TKLEIL39rzH5ajLbBiw4YUJRFHPEfaXvb762mpG7RpFh2od8Bvhl29hH7Z9GOP3jqfDmg7cjL1JU8emPEh6wLmIcyiUCnzsfOjh0YPZJ2aj1qip41CHVi6tCiXsJx+epMOaDrT4owUnQk/wResvCJscxpY3ttCxescKJeyQ29xjcrPJ3Jt0j80DN2OoZ8iIHSOos6wOu4J2UdRFkKGeIct6LWNlr5UcCTlCyz9aEpbybPhpQRjoM5Cfu//M7ju7mXZo2nOveRy2GJmsQACRyQo+3x7IzmuRLxz3524/Y29qz+hdo1GqlUWyMT8Y6xszvdV0Tj48ycmHJ4t9vopCxfoG/4dll5exLmAds9vNfqkvtCBlDDYGbmTM7jF0du/M7rd2Y6Jv8ko71Bo1w7YPw0jXiL1D9/JW7bfYf38/zZ2b41vFl4P3D7IzaCcArVxaUcu+FmqhfsWoz+fao2t0Xd+Vtn+25Xb8bRZ1WUTYlDDmdJhDFfMqhRqzPKGro8vg2oO59t41tg7aikZo6LelHx3XduRm7M0ijz+24VgODj9IeGo4LX5vwe2420Uab2KTiUxqMokfz//I2utrn3m/MKUCrI2tWdpjKddjrvPThZ+KZF9+Ges7FntTe749/W2JzFcRqLDifiXqClMOTqGHZ49XRplM6+qFsf7TW15jfV2mdfV66rW9d/fy9o63aePahh2Dd+S76JOuji6O5o55yRwx6THcT7zPgtMLeLve2zR3bs72oO303tSbjms70rBKwwKHG8akxzB612garmzI5ajLfN/5ex58+IApzadoLY6/sAghyFZlk6nMJFOZmZupWkruwsfoSDq84fMGNybc4Jfuv3A95jr1V9Tn88Ofk6XKKtLYHap14NSoU6g0Ktr+2ZbAmMAijbeo6yLaubXjvT3vPTNWQXedj+lfsz+9a/Rm9onZRKVFFcm+/GCsb8ykJpPYf3+/Vh6iMhU0WiY9J50GKxqQpcrC/z3/fMULv8pveTHyIu3+bIePnQ9H3zlaoCQTIQQT900kQ5lBbEYskWmR/NDlB74/+z32pvas7b82r5FGZbPK+ao/8xi1Rs3yy8uZcXQGmcpMPmz6IV+2+bJYasM/j9TsVG7F3eJO/B2Ck4IJSwkjMi2S6PRoEhWJpGSlkKHMeOZzOpJOXtkBOxM7KptVxtnCmWrW1fC08aSmXU08bDxKJKIDID4znmmHpvGn/59423qzrv+6IjdouZdwj/Zr2pOtzubkyJPUtKtZ6LFi0mNosKIBlkaWXBl3JW/HWJRSAcGJwfj86sPQOkNZ3Xd1oW3LL/GZ8Tj/6MzIeiNZ1mtZsc9XVpFDIV/C2N1j+f3a7xwfeZw2rm2KPN7D5Ic0WdUEU31Tzo0598pGCE+iERp0JB2SFElEp0fz4/kfebve27RyyW1qXGNJDX7t+SudqncqsF13E+4yatcozoafpVP1TvzS/Re8bL1e/cFC8jhz9XTYac5HnudK1JWn+qzqSDpUNa+Ko7kjlc0qU8m4ElZGVpga5JYf0JVyd0dKjZIsVRbpOekkZSXllRwISwnLy4QFMNIzon7l+jR1bJrXE7W42/35BfsxZvcYotOjmddhHlNbTC3S+cS9hHu0Xt0aXR1dzo05h4ulS6HHOvLgCJ3WdWJCowks7bkUKHqpgGl+0/jh3A/4j/enrkPdQtuWX0btGsXWm1t5NPVRifQGLovIoZAvYN/dfYJZiM8OfaaV8dKz00W9ZfWE5XxLcTvudr4+88fVP8TWm1uFQqnIe02j0QghhPjq6FfiwL0Dea/32NBDBEQHFMgmjUYjfr34qzCeYyysv7UWa/zX5I2vbSJSIsSyS8tE7429hfk8c8EsBLMQbovdxKC/Bom5J+eKXUG7xJ34OyJblV3k+ZIVyeJS5CWxxn+NmHJgimj9R+u8MEZmIQz+z104fTNc/HDsQLHdc2Jmohi4ZaBgFqLvpr4iJSulSOMFRAcIy/mWotbSWiJZkVyksSbvnyyYhTgWcizvtR1XI0SL+UeE22d7RIv5R14ZwvskCZkJwnK+pei3uV+R7Mov58PPC2YhVl5eWSLzlUWQQyGfJS07DZ9ffbAwtODquKtFLsAknkjb3jdsH908ur30eoVSQZs/2+Bp40lsRiy17GrRqGojRtQbkXfN2utrWXhmIYNrDeZA8AF8K/uypMeSfNuUnJXM6F2j2RG0g67uXfmj7x9UNa9a6Ht8HnEZcWy5uYWNgRs5F3EOADcrN7q5d6NDtQ60dm1NZbPKWp3zZWy7EsonO3eQIq6h0LlCtk4QSBqqmLoxvvEoRtYfWaQV8fMQQvDzhZ+Z6jcVb1tv9g7dW6SszmMhx+iyvgudqndiz5A9hQ6/zFRmUndZXXQkHQLeD9BKR63Zx2cz68Qs/N/zL/Ym9EIIai+rjZWRFWdGnynWucoq8sr9OXy0/yMhzZKKnPDzmOWXlgtmIeacmJOv6+/G3xVDtg0RQuSu+DcEbBDjdo8T225ue+q6vXf3itXXVos1/msKZE9gTKDw+NlD6H2tJ74/871WE3E0Go048uCIeOOvN4Te13qCWYi6y+qKOSfmiBsxN4ptlZwfWsw/8lSCmdNnG4TNFxOFxez6glkIndk6os+mPuLog6Nat/Nw8GFhOd9SVP6+srgefb1IYz3+ffryyJdFGsfvvl+Bfi9fRZIiSZjPM8/73S1u5p+aL5iFeJD4oETmK2uQz5V7hRH369HXhc5sHTH+n/FaGe9GzA1hNMdIdF3XNd8iGpIUIpwXOQv/R/5CCCHiMuLEH1f/EBP3ThR34+8KIXLdHIXJYNx7d68wm2cmKn9fWZwJO1Pgz78IpVop1l1fJ+r8WkcwC2GzwEZMOTClwK6i4sTtCWF/8sftsz0iJClEfHH4C2G70FYwC9HktyZi/739WhX5GzE3hOMPjsL6W2txOfJykcYatXOUkGZJ4nDw4SKNM2DLAGE611REpUYVaZzHfHzgY6E7W1eEp4RrZbyX8SDxgWAWYsHpBVofuyguqteF/Ip7hQiFFELw0YGPsDayZm7HuUUeL0edw/AdwzE3MGdNvzX5PlBzs3JjUpNJrLiyguSsZGxNbGnh3IIsVRaxGbFciLjA+oD15KhzCmTPqqur6L2pN542nlwae4kWzi0Kc1tPodaoWR+wHu9fvBmxYwQaoeH3Pr8T+XEki7ouoo5D0Rp5aJOX5SG4Wbkxt+NcwiaHsaznMmIzYum+oTvt17Tn6qOrWpm/ln0tTo8+jaWRJZ3XdSYgJqDQYy3pvgQvWy/e2fkOyVnJhR5nQacFZKuz+ebkN4Ue40kmNZ2ERmhYcXkFO69F0vLbo1SbvpeW3x59aUJUYahmXY2GVRqy/fZ2rY5bmISuskyFEPe99/ZyPPQ4s9vN1kqZ129Pf4t/tD8re68sUGQMwICaAzDVN2XRuUUAeNl6YWtiy7mIczR1asrUFlML1BT5h7M/MPafsXRx78LJUScLXYbgSU6EnqDRb40YsWME5obm7By8k4D3AxjdYLRWfLjaJj95CMb6xoxvNJ47E++wtMdSbsXdotHKRkzaN4m07LQi2+Bm5caxd45hom9C1/VdCU0OLdQ4pgamrOu/juj0aKb5PT/rND942HjwboN3WXV1VZEzYSH3/np49mDpxd+Yvt2/2AWyr1dfLkZeJDYjtshjPX4YTd7iX6jer2WVci/uGqHh8yOf42njybiG44o8XlB8EHNOzuGt2m/Rz7tfgT/vbuPOm7XeJCotimHbhxEUH8ThkMN5pVsLErf9/dnv+eTQJwzyGcSut3YVORkpPjOet3e8Tbs17UhUJLJxwEaujLtCX+++r3U5gn4NHJk/oA6OVsZI5MZwvyjUz0DXgAmNJ3B30l0+aPwBSy8tpe7yupx6eKrIdrhZueE3wo8sVRa9N/Uu9EOjUdVGfNz8Y1ZdW8WZsMIfKn7R+gsEgu/Pfl/oMZ5kTIMxJGXHkKR+OhCiOASyu2d3BAK/YL8ijfPkav1FvCqhq6ySr2+sJEndJEm6I0nSfUmSpj/nfRdJko5JknRNkqQASZJKptp/Pth6cys3Ym/wdfuvi9yFRwjBpP2TMDUwZXHXxYUep7FjYxZ3W4yxnjHfnfmOPjX6FLjV2PLLy5l2aBqDaw1m48CNRW6QsfvObnyW+rD5xmZmtJ5B0AdBDKkz5LUW9Sfp18CRM9M7EPJtT85M7/DKGG4rIyuW9FjC6dGn0ZV0abemHfNPzS9yZqyPnQ9bB23ldtxtxuweU+jxZradiZOFEx8d+AiN0BRqDGdLZ4bWGcrv134vkovnMT08e6AjzMjQfba4l7YF0reKLzbGNhwJOVKkcZ5XfuG/vMitV9Z55TdXkiRdYCnQHfABhkiS5POfy74E/hJCNADeAl6LtioaoWHOqTnUtK3JIJ9BRR5v953dHH5wmK/bfV1gd8x/MTMwY1WfVazovSKvq1J+2RW0iwl7J9CrRi/W9V9XpCzNbFU2E/dNpO/mvjhZOHFl3BXmdJhTINdQWaaFcwuuvneVN2u9yRdHv2DI30OKXF6gU/VOzOs4j623trLyyspCjWFqYMq8DvO48ugKW29uLbQtk5tOJlOZyRr/NYUe4zGGeobY6rYiU/cCgqcLimlbIHUkHdq6tuVEaNGqRL7qofO8MiLlhfwsy5oA94UQD4QQOcBm4L9VtgTwON/eEij+YhT54MD9A9yIvcH0VtOLXLZVpVEx/ch0vG29eb/x+4Ua43k1UwoqzNejrzN0+1AaOzZmyxtbirQbiU6Ppt2adiy9tJSPm33M+XfPa+2g9NdLv+K62BXXxa48Snv0wuuyVFm0/bMta6+vzVuhBicG894/79F3c1+Ohx7P+zcT/8aWf3zwY3YG7dRa/RkLQws2DtjIgk4L2HJzC93WdyuyH/6TFp/Qxb0LH/t9zIOkB4UaY1jdYdSyq8XsE7MLvXpvUKUBTRybsOraKq38e41p9CZCyiRL53/1X4pLIFu5tCIkOYTo9OhCj/Gyh87L3HflgfyIuyMQ/sTfI/597UlmAcMlSYoA9gGTnjeQJEnjJEm6LEnS5bi4uEKYWzB+PP8jjuaODKk9pMhjrQ9YT1B8EPM6zCv0SnnOyTm0W9Ou0CvD5Kxk+m/pj7WRNbve2pWvipMv4nbcbZquakpATADbBm3jh64/aLX3aXOn5uwfth9rI2tUGtUz7z8Wq08PfUp0ejQpWSl55WUn7Z9EjUo1eKvWW8w8PpOI1Agg9yD7evR1bE1sWXJxCf7R/lqzV5IkPm35KRsGbOB02Gm6b+hORs6zNW/yi46kw6req9CVdJmwd0KhhFVH0mFG6xncjr/NP3f+KbQtI+uN5EbsDa7HXC/0GI+Z0fFN9HQM0DO5/srzjaLS1LEpkFu3qbC86LB98eD6+XLflWXyI+7P66n239/UIcCfQggnoAewTpKeddYKIVYKIRoJIRrZ2RVvDZCg+CAOPzjMhMYTiuxrV2lUzD01F98qvoU6RAUISQphwZkFOFk4FSriRAjB2H/GEp4aztZBW4uUAXrt0TVar25NtiqbU6NOMdBnYKHHehENqjTAxdIFHUnnue8tgpAAACAASURBVA9DHUmH/fdyxb+5U3PMDc3R19XHP9oftVDzXqP3GFJnCNZG1nlf7jXX1/BZq8/4ovUXdKzWkZ1BO4vsQvkvQ+sMZfMbmzkXcY5BWwc998GUX5wtnfm6/dccDD7I3nsvbkL+MgbVGoSLpUuRSu8OqjUIXUmXv27+VegxHmNqYEprl5bY293L9/lGYalfuT4SUpFCVgty2F7eyI+4RwBPdvZ14lm3yxjgLwAhxDnACNBO595CsurqKvR09BjTYEyRx9pxewf3E+8zo/WMQvcPnXF0BjqSDgs6LSjU5zcGbmTbrW180/4bmjs3L9QYkNsrttO6TpgamHJm9Jli7bSj0qjQCM0LdwTzT8/nXd93MTcwR6lWoiPpcPXRVRpWaZh3TUvnltxPvE9wYjB2pnbYmeQuCrq4d+FG3A2yVdlat/sNnzdY3nM5++/vL1I4IsAHjT+gRqUaTD88vVCuFT0dPcb5juNY6DHuJ94vlA22Jra0cW3D7ju7C/X5/9LWtS3Xo6+TkpWilfFehKmBKR42HgTGFq0kckEP28sL+RH3S4CnJEnVJEkyIPfA9L+/JWFARwBJkmqSK+7F73d5ASqNivUB6+lVo1eRDz4BFl9YjIeNB329CtfcODAmkE03NjG52eRCxaHHZ8bz0YGPaO7UnGktCi824SnhdNvQDSM9I469cwx3G/dCj5UfNEKDQDx35f7Zoc+Y3mo6zpbOeW0FIdcHb6BrkPcZPR09VBoVyVnJWBpa5j1cDXQNUCgVxRbN8//snXdYFGfXh+/ZZekgvYi9Y+8Fe+8tscQWTaImMZpi1M9XTWyxJsYkr77RKGqMxhbF3mvsigURERUbghRp0mF3n++PzRJEyjK7aKLe18V16TJzZmZ3OXPmPOf8zqgGoxjXeBw/nP8he1CKHFRKFTNazyAoJki2neF1hyMhse7aOtnn0b1yd4JigghLDCt840LwKe2DQDdovLip7lrd6IEmryuF/mUIIdTAWOAAEIyuKiZIkqRZkiT1+muzL4FRkiQFABuAEcJUq10yOHL3CFEpUbxb+12jbQVEBnAm7AxjGo6RvSg799Rc7MztmOAzQdb+U45MITEjkRU9VxglKNVrYy+SM5M5MPQAFRwryLJTFDRaja4NOocD1kevG4M2MuHgBJqsbML6wPWMPziefbf3Ya2yJjUrNTtHnZSZhK25Lc7WzjxJfYKF0iL7eqxUVkan3Ariu07fUd+zPqN3jSY2NVa2nQE1BlDBsUJ241pRKWVfipZlW/LHjT+KtF/OTtLfjuvqHY7fPy7rHHLSoKTuycpUHb4FUcW5CqHxobIXlF9nDAp7hBB7hRBVhBAVhRBz/nrtayHEzr/+fUMI0VwIUUcIUVcIYVzngZH8ceMP7Mzt6Fq5q9G2fK/4YqG0YHjd4bL2f5DwgM1Bm/mo4UeyumODooNYeXklYxuNpYZbDVnnAPDpvk8JiAzg97d+p6ZbTdl2ioJCUqCQFM/ocusd/an3TvHHgD/w7eVLs1LNGFZ7GHU86tChQgd23dqVXYrpd9MPn9I+lHMoR1RKVPZgj923dlPPo55JF4FzY640Z03vNcSnxzPlyBTZdpQKJWMajuF02GluxNyQZaNP1T4ExQQZ3Pmau9U+/qkHCmHN+iuHZB0/J05WTnjZeXE9+rrRtgqjvEN5MjWZRlXMvK78OzpUioBWaNl5ayfdKnczulVerVWz8fpGelXtJVu2YJn/MgDGNc6zgKhQZpyYga25LdNaTZO1P+jq4n2v+DK5xWS6V+ku205R+GDHB9ReVptrUdcovbg0q66swveyLysurQB0i43VXatT060mlmaW1HCtQUm7kpSyL0WXil3o8XsP+m7qS12PutTzrAfo8tfj9o1j8uHJnH10lkE1i7/JqpZ7LT5p9Akrr6zk5pObsu0MqzMMpaRk/bX1svbvXKkzoHsqBQrVd8ndvCOhwFxbiVMP5Vee5MTb1ZuQ2OJv29enMfUVU28wnBczo+wF4h/hT3RKND2r9DTa1on7J4hJjeGdmu/I2l+tVbP66mp6VOlB6RKlC98hFyFPQth6YytTWk4xaBRgXiRlJDFm7xjquNdhRpsZsmzIwbe3L2qtGo1WQ6YmE3OlOVqhzXOw97z2856RTvi69dccu3+MTE0mbcu1zc6/j2s8jl8u/UJ8ejyTm08u9jUDPVNbTmXF5RUsOL1A9rg5Nxs32pRrg99NP1nidd4u3rhYu3A67DTOUpdnpivp9V2A7MXCvJp3VKI8ydr92dO/jKGiY0W2Bm81yoYh6KvCopKjiv1YrxqvnHM/FKp77OxUsZPRtnaE7MDKzKrQIRz5oc/9j6gzQtb+Sy4sQaVUFTnqzznvVW27gQhNBFsHbC2WFIZaq2b6sel83Ojj5xaLzRRmmCnMCh2KknvIhaOVI295v/XcdhZmFoxrIu8JyBhcbVwZUWcEK6+sZFGnRbKf4rpX7s74g+MJSwwr8s1ekiQalWyEf4Q/IcHPt9Tr9V30zr2kg9VzeioqbWmEWQZhiWFGDRYBKG1fmiepT0jLSivWbmZ9UBObJn/N43XllUvLnHhwglputUwyS3P/nf20K99OdrPQ1uCtsnP/6ep0frv2G/2q9ytSxU/OXKuaRMLVf2CnbU1kTNGfHAojU5NJ/y39mXtqLn7Bfia3X1SWXljKvfh7hW8og5H1R5KpySzyomZO2pRrA8Cph6dk7V/bvTY3n9wkPCE5z9/njNbzat6xUXoCyFaszEl2RJ1SvBF1CYsSAMVedvkq8ko5d41Ww7lH57KHSxvDo6ePuB13m/bl28vaXwjBntt76FKpi6zc/77b+0jMSCxy1J8z15pkthchZWCbOdDkqn1CCN7b8R7bb27nxy4/vpSIOiexqbFMOzaNflv6FVkP3xDqetSlomNFo2rFa7nXwkJpIbvKpLJTZbK0WTiXyFsaIWerfV7NOxM76PojIpKMVwfRR9TxafFG2yoIG3MbQFcd9Yai8Uo591uxt0jKTMpuWzYGfXTVulxrWfsHPwkmIimCzhU7y9rf76YfTlZOtC3ftkj76aM3gYZk5QEsNfUwF2VMrtr34/kf+T3wd+a0m8OnTT41qW05OFs7s7r3ai4/viy75LAgJEmiY4WO/PngT9lleWYKM6o4V+FmrLyFWX0q5+1GVoXq18PzzTsDG+iqrUyR4tCvkSRlGq+FXxD6VGJx3LBfdV4p567XGtFXVxjDhfALWJpZUstNnpCWXh9czs1BCJ2OdZdKXYqsY6OP3jIUwWgUT7DVdHzmdVNwL/4e/znyH3pW6cl/WvzHZHaNpU+1PnSv3J2FpxcapQuTH429GpOUmSS7UxR0mu8PEh7I2lffnevtJclqqbe30NW6m2I4if5ptDg6hHOiX/h9U+dedF6pBdWgmCCUkpJqLtWMthUQFUAtt1qym2T8I/xxsnKiomPRKzruxN0hKiWK1mWLfmOY2Lkq/9kWSLy4AMIMK00jk6v2zTgxAwmJ/3X/X6FyDDkXd0s6WDGxc9Vibf+e1HwSrde0ZvvN7QypPcSktqu66N7D0LhQqjhXkWXD3cYd/wj/wjfMA71zTs5MZlg9ryK/j6aMgl+U09Xb/7fMFfgn8Uo599txtynnUM4kVSE3n9ykY4WOsvcPjA6kjnsdWVo0lx5fAnSRYlHR/8EP2xWMhboqpR2cnnGohjrbadsD2XA+DI0QKCWJQU1K802fWsSmxrIhcAMfN3y+OiY3+sXdgkr2TE2LMi1wtXbl0N1DJnfunra6BUljFhFtzG2yG7GKiv4pTq6YmfSXBqB4Tvev6Gi0us/UWCntwtA/GRRWcfWG53mlnPv9hPuUdyxvtJ20rDQikiKo5FRJto3bcbcZUH2ArH1vxNxAISnwdvGWtX/POh6o997jkyZjWNS5Xfbr+Tlb/wdxHLsZk+3wyzlbcTo0Lns/jRCsO6ebw+ld4RpZ2iyG1h5a6HnkNQUnd8meqVFICup41CH4ien1SPRVU8Ys7ikkhexoV98jIDeK1Ufspgh+0tS6NZzinqmrvxEaI2/9uvJKPeuEPw03yYDo8CRdt19pe3nlgymZKcSlxcmuJX6Q+AAvOy/Z0cqqs5dIV6fz65+Zz3Qv5uds1597+MzA45yOPScbzofhH+GPtcraIDXJ/BZxi3tmpaOlY7GUzumdq1KSH62mZaXJdoj6dQS5jk6/+GnsrF2ApxlPgb9TRcWF/nPUl0S+wXBemchdCEFMagxu1m6FbltYaiImRSdoqVcqLCr6ie3uNvIUKaOSowzWa899LW2rubLu0lkwA4VweiYVkp9TNfQhXSMEEckRlLIvZdDjeF6NNPrjNZ9/tNjy708znj6jZ2Mq4tJ0Nz0HSwf5NtLjZDdB6atc5HYrP0l9otvfSt7+xWWrIIy95teZVyZyT1OnkanJxNHKscDtcgsq6Z1fTm0O/TDhwmzlR2LGX9GGpbxoIykzyaCIKK9rWX/uIekanUOV0EX++lSIsRUzyiKuH+TVSKMnr/fdFAghuB59ncpOlU1qF8iucilTooxsG2GJYXjZybuhhT/VvVf63H9R0Y879LSTt39uWxKS7ADIUPSCYXIDpdeZV8a56x9ZbVQ2BW5XUB44+/9/5ROtzOQ5Q31uUy9PW1Q0Wo1BkXFe16KLwvVO+O/cbkRCWp7OtijuelCT0pSyK0VYYphBi3o5G2nyIvf7bgquRF4hPCmctuWK1h9gCNeirgE60Sw5CCEIiQ2RvZYTGh8K6Mop5aDvTC1bwjjpAYCHTx/iYetRrJLL8LdgmCnSra8br4xzz3aoheSpDckDG1sJYGxVgkqpMqhcLb9rUQhdTlUr/d2mXtLBKs+uxSFNy+QbXefEWqXgmz61aOTViDR1GhfDDRvUoG+kKeo1yOW/F/6LpZllsYwOPBV2iqrOVWWnZR49fURcWhy13WvL2j8oJojyDuVla7mExIagUqiM1pUBXTmoMQUHhnIv/h4WSguTDN153XhlnLuh5JeayPm63qnrnXxR0S+YyZ3v6WDpkJ0aKoj8rsVM6CYcqiVdyZ6ELg3SfP5RgGe6FhuWdcJSVfjX4K0Gpdh+JZw5Wy2QhDmdfplBvVkHDUqrbL8Snu8Tgimbq648vsLagLV81ECedn5BpGalcuzeMaPKY8+EnQGgaammsva//PgydT3qyj5+YHQg1VyqyR7wrkcIQfCTYKo6m653Ij9ux92molPFN3XuMnhl3jH9FzZLk1XgdvlNQ8/Z5GNsyZs+spOru+Fp62mQfnV+1/Ju0+qY40ymdA+JvxdMc+e59Tn7+NSC3zOAPdceM3FLAElp5thoOpKsPEJ02l0m/hFQqIP/9kBIns8w0l/XYAqSM5MZ6jcUNxs3vmr9lUls5uTco3Okq9ONeiI4GHqQEhYlZDnoqOQo7sTdkX1jEELgH+Fvkpm5kcmRPEl9Qi13ed3bReFGzA2TNCW+jrwyzl3vkPX58vwwZBq6vuwqPl2ec9YvMj1Ofixr/0pOlXiS+oT1F24UOJAhv2v5pk8teni3Rm0WjDaXW82Z584rZ58f8alZZGl1thyyBqHAiifm35OpySg0b15Qlc7MXUGUm7yHcpP3UHemYU8CudGrU958cpPf+v5m8qgdoF35dtz97C6tyraStb9aq2b37d2yJCUAjt7TPXXplSWLSmh8KNEp0bJvDjnRd9gW53B10K2j3Ym7Q203eWms1x2DvmWSJHUBfgSUwEohxPw8thkAzED3NxsghBhswvMsFBtzGxSSwqD65j6FtG7r83tyBwRYmFngaevJvQR58rN6PZspu3YjZenEnvLr7sx9LfoJPSFJJck0jyZLeoC5KPeM/YiENLZfCc+zTNEQlDjgnPk5MRbf8MT8O6SESQVun19JJPDMU0NCWhYTtwRkX5chPM14yoAtAzgQeoAVPVfQoUIHA6+i6MhdyASdc45OiaZ/9f6y9t97Zy/OVs408Gwga3/97FQ5kha5OfvoLGYKs2J37gFRAQiEUamo15lCI3dJkpTAUqArUB0YJElS9VzbVAb+AzQXQtQAPi+Gcy0QhaTA2cqZmNQYo23pS9UeJj6UbaOaSzXZU9sbeTUC4KkIeub1wqpLcpZGWmmagFCQojz23HYO1qrsG4UhWKmUOFg9WxVhrW2KY+YoUpVnSLSeU+AaQVGqdLK0wuAKmoDIAJqsbMLhu4fx7eXLyPojDdrvZbDi8gqcrJzoUaVHkffNUGewK2QXPav2lL3Iv+/OPrzsvEyS4jjx4AQNPBsUe9fohXDdSED938MbioYhaZnGwB0hxF0hRCawEeida5tRwFIhRDyAECLatKdpGJ52ntndpcZgYWZBafvS3ImXr/5X2702gdGBsnRAXKxdUGnLkaa4+tzvCqouyZlmUeKIlbYJyWaH0PL3wq6VSokQ5JuOsVIpGdq0zHOpnhm9aqBSPOuS7TW9cVV/ShJXqLe8XnbqIDd5pY8KqiMqrIImKSOJqUem0mhFIxLTEzn87mHer/d+gfu8TB4mPsQv2I/36r4nq+t4963dJGYkMrDGQFnHT1enczD0IN0rd5eldZSTpxlPOf/ovOw5B0XhdNhpypQoQ0m7ksV+rFcRQ9IyXkBYjv8/AnILplcBkCTpNLrUzQwhxH6TnGERKFuirOxUSG68Xb2Nmu7etFRTfjz/IwGRATQo+fejtKHCXW6qZoSrN6HhKUr+bmgqqLokt1O0V/chyuIsyWb7KKHum328LzY9f9PQU5h07IydQSSk6VIpjtYqfug5CQ/XQQzdNpT2a9vztvfbTG89/bnFttzpo+bzj+abqsnvGhPSE1hxaQXfnf2O6JRohtUexvedv8fF2iXf8y0qYYlh/HT+J9qVb0cV5ypUdKqIEMIop/jt6W+RJEm27r3vFV9K2pWUXamz/85+kjOT8xxdWFQOhR5CIzTZA7uLCyEEfz740yTjMl9XDInc8/pW5w68zIDKQBtgELBSkqTnioElSRotSZK/JEn+MTHGp09yU9mpMnfi7phEhrSue12CooNk61XrF96O3DuS/Zoh3bF6xrcYDpKWVOXfI9kKk+7N7RQttTWw1NQjSbWZi1834fTkdvSp55Wv8/T6qxY+P/rU8+Lq9E7cn9+d+/O7c+XrTvSp50XTUk0J/DiQmW1mciD0ALWX1abD2g6su7YuW4MkNxM7V0WlfP6rpVJIz1xjhjqDfbf3MWL7CLy+92LS4UnUdq/NuQ/OsbbvWpM69ovhF2m5uiWSJLHr1i4mH5mMf4Q/kiTJ/k7dT7jPL5d/YUSdEbI6W+/E3WH/nf2Mqj9Kdkpm3bV1uFq70q58/v0GhrI9ZDuOlo74lPYx2lZBBEYHEp0STbtyxp/z64ohzv0RkFNBqxSQe07XI2CHECJLCHEPCEHn7J9BCPGLEKKhEKKhq6vxM05z4+3qTbo6nbvxd4221aRUE7K0Wdnyu0WlpF1JarnVYu/tvdmvGdIdq+eL1p0oZ1+ddIsDgDBoIENeuW1PMRohpfHlwS8L3M5YzXcrlRVft/6aB58/YE67OYTGhzLMbxjOC51ptboVU49MZVvwNoKig0jOTKZPPS++7VcHR+u/c/l2Vll82sUKrC4y8/hMOq/rjNNCJ7r93g2/m34MrjmYy6Mvc2jYIZqUMn7aVm6SMpMYVHMQCzsu5Jt239C+fHvG7RtHhjoDhaRAiKI3pU06NAmlpGR6m+myzmnRmUWolCo+bPChrP1jUmLYGbKTIbWGGN1Nqs/996ray+ha+cLYf0f34P8mcpePIZ/QRaCyJEnlgXDgHSB3Jcx2dBH7GkmSXNClaYz3sEVEv6p+5fEVo7vn9HNYj98/LjtK6VOtD3NOziEqOQp3W/ciqSRKksSUVp8zevdofEdb0b5C4RGM3vE/m/bpyaX4cL45+Q09Kvegf43++WwnT8QrrzTTlJZTqGYzjOn7/XiY+ieXw65zOmwBWvH3jc3SzBI7czvMbMxQW6lJykzigTqdT/9a/5WQqOlWk/frvk/nSp3pUKFDscjLpmSmZM/pjEiK4Fz4OQCcrJz4qOFH+Ef4M/7AeJZ2X1rk1MzB0INsubGFmW1mymqfD0sMY9XVVYyoM0K2HozvFV+ytFmMajBK1v452XN7D4kZiQyqOchoW4Wx+9Zu6rjXwcu++Aa7vOpIhkQjkiR1A35Al09fJYSYI0nSLMBfCLFT0n3rFwFdAA0wRwixsSCbDRs2FP7+8ibS5EeGOgP7+fZ82vhTvu30rdH26i6rSwnLEpwYcULW/jdiblDjfzVY3Hkxnzf9PN88s5eDVZ4t+unqdCr8WIHKzpU5Pvy47LxvliaLVmtacT36Omc/OEtNt5qy7OQmtz486J4A3m7gxdZL4c+8bqHKYlQ7c7xcEgl7GkZMSgzJmcmotWrMFGbYWdjhYu1CKftSVHKqRHXX6iaRpi2I7858x8mHJ/Gw8WByi8mUdyxP81XN6V21N5Oa68o778TdYerRqcxsM7NIlSaJ6YnUXlYbKzMrAj4KkLWQOmrnKH4N+JXb427nKxlQ0BpOpiaTCj9WoKpLVY68eyTP/YtCrw29uBhxkbAvwoo1co9OicZzkSdTW05lVttZxXacfyuSJF0SQjQsbDuDPiEhxF5gb67Xvs7xbwGM/+vnpWFhZkHDkg05FXaq8I0NoFvlbiw8vZDY1FhZkqPVXavT2Ksxv1z6hc+afJY9Ai+3M8wvHWJpZsnUllMZu28se27vkVVGBzqtmi39t9BoRSO6/96d0++fNokQU35pJv0Ep5xkZKnwO2/J6cndjD6uKThy9wjrA9ezpf8Wll5YyqKzi2hTrg2req3irc1v0apsK5qWakpJu5JISEW60Qgh+GTvJzx6+ojT75+W5divRV1j1dVVfNr40wIde0GTrtZfW094Ujgreq4o8vFzE/40nL239zLBZ0Kxp2S23tiKVmjpV71fsR7nVeeV6VDV06ZsG/wj/PNdyCsKb3u/jUZo8LvpJ9vGxw0/JvhJMIfvHjaoOzY37sruWEml6bt+NM3m7ZctkVvKvhR7Bu8hPi2edr+2y5aPNYb80ky5HXte2+ubrfLrvi1uQmJDaFG6BZWcKjGz7UxalmnJ/jv7ScpM4qtWXzF462BOPzzNzpCdhMSGFGmo9IrLK1gfuJ7prafL6gjVCi1j947F0dKxQCmFgtZwsjRZzDk5h3oe9ehSqUuRzyE3y/yXoRVa2bn/orDh+ga8XbxlD6d/g45XZliHno4VOzL31FyO3jtKn2p9jLJV37M+lZ0qs+7aOtkNMoNqDuI/R/7D/NPz6VixY6HdsTnZfiWcr7bfxE7zIdEW07iRspL/bNOdR24beQ3tyDk6T/e4Xp99Q/bRZX0XWqxuwYGhB2QPeob8O0+VkpSngy9hpcpOTeWleZPXdZmSBwkPcLJyws7Cjrbl2vJ74O8ERQdRw60Grcq2IjI5Er9gP+a0n8OT1CfsvrWbo/ePsqTrEoNlfk89PMXYvWPpXLEzU1tOlXWeKy+v5OTDk6zsubJAKYWC1nBWX11NaHwoO97ZYXRte2pWKj/7/0zPqj1NMsayIO7G3+Xkw5PMaTfH6PN+3XnlIvfmpZtTwqIEO0N2Gm1LkiRG1B3BiQcnuB17W5YNCzMLJvpM5Oi9o9kt4Iaij8ystHWxVXfiqdk24jVXn6uuyavEcl2u0Xn6ksvmZZpzbPgxUjJTaLqyKYdCD8m6Lsi/6mZQk9LPva5SSKRkqrNvBrldf3Fou+uJT4un3+Z+fLj7Q97a/BaH7x7G29WbjhU68mvAr2RpsvC088Tb1ZugmCBd5Nx4LPM6zOPsB2dpXqa5Qce5FXuLPhv7UN6xPBve3iCrdPF+wn0mHJxA23JtC23Myq+k1b2E4OtjX+NT2oeeVXoW+Rxys/rKamLTYvmy2ZeFb2wkvpd9UUgKhtUeVuzHetV55Zy7SqmiR5Ue7AjZUahCpCG8V/c9zBRm/O/i/2Tb+Ljhx3jZeTHp0KQi1UvnjMwcs0ZhJjx5Yv4tDxOerUQ1RAAsp/NsWLIh50aew8vei87rOjP92HRZnbT6NFPOckYLMwUNyzo9l36ytTQjS1Pw4n1xzFZ9mPiQnht6Utu9NjsH7WRA9QFMOjQJtVZNl0pdSM1KZdHZRYCu7C4+PZ5bsbey9zdUajYsMYyOv3VEISnYM3iPrCleaq2aodt0g8dX9V5VaOSa3821ZJm9RKVE8X2n742OfjPUGSw4vQCf0j60LNPSKFuFkaXJYtXVVXSt1JXSJeTNL37D37xyzh1gYI2BxKXFceiu/KhUj6edJwNqDGDllZUGaaznhZXKirnt53Ix4iK/Xv3V4P1yRmYKrHDNnIKWFBKs55KW9bcjNNQp5tyugmMFzn1wjmF1hjHrz1n4+PoQGGW43kxO0rP+vmElpGVlp1hy6sYnGCArbEptdz2ZmkzGNh7L162/xlxpTv8a/bP7Iep41GFwrcFsv7md/zv0f/Tf0h8rM6sij7F7mPiQtr+2JSE9gf1D98suw/3q6FecDjvNsh7LDBIpy2sN56MOKnbdXcGIuiNM0guw4vIKwp6GMaP1jGJPk2wN3kpkciRjGo0p1uO8LrySzr1zpc44Wzmz+upqk9ib5DOJ5Mxkfjr/k2wbQ2sPpXnp5kw8NDF7gHZh5I7MzEU5SmonkiJuMmTbkOxhIoY6RQdr1TOLmIeCEvi1z69s6reJewn3qP9LfSYcnGCQsqYeQxuzCjtHlUIiNVNt8gXWSk6Vnmnbz1Bn4B/hT3xaPJZmlviU9mFTv01Uc6lGHfc67B+6v0izb2/H3qbV6lbEpMZwYOgB2UqJW29sZf7p+YyqP4rBtQoXVNUvSOulJBYPrMufk1qz4fZUSliUYGGHhbLOIydJGUnM/nM2rcu2Lla1TdBVGH1/9nsqOVUyyQLwG15R526uNGdYHlq68gAAIABJREFU7WHsuLlDtmxvTup41KFX1V58f/Z72QM4FJKCX3r+QlJmEh/v+digbse8IrMlfT9icefF+N304/2d76PRagocRK1HpZRITlfnmYcfUGMAwZ8EM6LOCL4/+z0Vf6rId2e+M2hYSX5PDeEJac846oKUIR2sVCDp5H8Lk2UwlJzvb84y1ixtFh62HtmP/dEp0ZR1KMt79d5jWqtpRTrGhfALNF/VnJSsFI6+e9SoCUvvbn+XpqWa8t+u/y10+/xkLN774yvOh5/np64/4WpjfAf4gtMLiE6JZkGHBcUetZ98eJKLERcZ33T8m6lLJuKVfRc/bPghWdosVlw2vsYXYHbb2TzNeMrck3Nl26juWp1v2n7DtuBt+F7xNWgf/QxSfXqjTz0vPmv6GbPazGJtwFo85nTm803+WJgpcLRWZd8Ecis72pibZQ/b0JMzwnaxdmFFrxX4j9ZN65l4aCIl5pbEcdoQGs3bmq+jLSgiz+l4gOduVIsH1uX+/O7YWDyfj5ezwDpu7ziWXFhS4DYSElWcqpCYnkiP33sw64S8JpmN1zfSek1r7CzsOPXeqWfE4YrC/YT7dP+9Oy7WLvgN9DOoJj6vp6UEdQjrgr/lbe+3TdJBGhoXyndnvmNIrSHFIvWQm2/+/AY3GzdG1B1R7Md6XXjlSiH1VHOpRpdKXVhyYQkTfCYY3bpe2702I+qO4MfzPzK6wWgqOz8nnWMQX/p8yYHQA4zbN46GJRvKHkRQy/59XDV3iWENKeaJaNP+DxuVLYsH1s2znLD85D152skdedf3rM+YmqsJubWRGGkTCarf8c/YzLvbffgiejRfdRz4TBNLXo1ZudE7av3NKTf5qUMaOkwkU5PJkG1DeJDwgOMPjlPXoy4tyrRAo9U8V7ES/CSY9YHrCYgKoEeVHnzd+ut8rOZNliaLyYcn8/2572lZpiVbB2yVHSU/TnpMx986kqHO4PCww3jYehi0X+7PTEsqT8wXoNA6sLzHcqOjbCEE4/aNQ6VUsaDDAqNsGcLZsLMcunuIhR0Wyh7+/YbneWUjd4AJzSYQlRJVpEXMgpjbfi5WKivG7B0jS0QKdOmZ9W+tx9nKmT4b+xCTIk8d89sDIVhn9sMpcyxpistEWkwiSf2YzzddzTNnbchg8Jy2paxquGVOp2T6Muw03UiRLjPr3FAsZrli/1U33KfMpOm8fcDfEXlB5JW+0eeN80NZiJPSfwbmSnPGNBzDoWGH+LLZl0w8NJG0rDSUCiUareaZz0qtVVPVpSoLOiwosmO/F3+PVmta8f257xnbaCyH3z0s27FHp0TT4bcOPE56zJ7Be6jhVsPgfXN+ZgJBrPkPqKUovC2myuqkzs2moE3su7OP2W1nvxBtl2nHpuFq7fpmIdXEvNLOvV35djTxasK8U/NkS/fmxMPWg7nt5nL47mHWBqyVbcfd1h2/gX5EpUTRe2NvWYO49c7STtMFt8zpqKUoHlt8TpriUp4566IoQeZ0xCpRCqes0ZRK/w3XjClYamqSrDxGtMUMLmT0Ycj2HmwKWczMAVrcS+RfTpn7JpIzb5wfORuhhBCEPw1nx80d/Ofwf2ixqgVd1v+98Na2fFtKWJbg3TrvUsutFmP26hyFUqFEkiQS0xO5FnWN1mVbc+q9U7Qt3zbf4+ZGCIHvZV9qL6vNjZgbbOq3if92+y/mSnODbeQkIimCNmvacC/+HrsH76ZZ6WZF2j/nZ5lotpFU5RnctB8wu6u8EX45iU6JZuzesTQq2YhxjccZba8wDoYe5Oi9o0xtOTVbwO0NpsEg4bDioDiEw/LiwJ0DdFnfhf92/S9jG4812p5WaGm9pjWBUYFc+/iaLI1uPVtvbKX/lv50r9KdbQO2FUmSNbcIWZYUToz5XLIUD7DPegsH9TBKOdg/I0hm6KCQggZpAAgySVcEkqa8TLoigCzFA/RtSUqtO+aiDGaiJGZaD8yEG0rhzKwezXinoTe25rZIkvTcMQQatKSglZLQSAlopFhsrOLpXEciJDaEoJggnqQ+AcBMYUYDzwZ0rtiZmW1nPnd+kcmR9Nvcj1H1RzG87nBux97m+P3jVHGuQutyRZshGhoXysd7PubQ3UO0KdeGNb3X5Kv1Ygh34u7Q6bdOxKTGsHvQ7iKfj57tV8L5v73LuaWejauiA8u7r6ZvfeP0goQQ9NnUhwN3DnBp9KUiPU3IQaPVUP+X+iRlJBH8SbAsDZ7XEUOFw1555y6EoN3adlyPvs6dcXeKVOaWH6FxodRZVocGJRtw9N2jsocoAPx88WfG7B3DgBoDWP/W+ux8dl6OGP6W6S1hpSIlU/3MQqSWdOJVK0k2249KWwaXzM+ImPeslpshDj4vtceC0JKM7ygnRm7YxJOM22QpHqKWHiOk55+WJCQszSxJz5KQkBBoEWSBlHfU72zlTFWXqlR3qU5t99rU96xPfc/6heZmAyIDGOY3DE87T2q71WZS80lFSqGkZqXy7elvmX96PiqFivkd5vNRw4+MquQ4/+g8PTf0RCu07B2yl8ZejWXbOvngJB1/60jDkg05/O5hk8ghL/dfzkd7PmJRp0WMb1b8GoD6423ut5n+NYx/6nhdeOPcc3D58WUa/tKQL5p+waLOi0xic23AWoZvH87UllP5pt03Rtn67sx3TDw0kX7V+7H+rfXsvRbznHNVKSUQPFPxolJI2FqaEZ+rQShNcZFY8yVopDg+aTSG2W1n42jlmK9Er168LKfjL2GlQpIgITULRT5aMXq8/rpJ5BzBJxBoiEcjxWBp+ZRudWwo5wrJmcmkZqWy/sJdkjOyAAWSUCFhgUJYo8AONxs3PmzegPeaNsbewj7f4xbE7djbNF7ZmI4VOrL+rfUGPxVptBrWB65n2tFphD0NY2CNgSzqtMjo3PPG6xt5b8d7eNp6sn/ofqM0fQIiA2i9pjUeth6cfv+0SfLsgVGBNF7ZmFZlW7FvyL5iL0eMTY2l6pKq1HCrYZSc9evIG+eei1E7R7EmYA2XR19+br6nXEbuHInvFV/8BvoZLVK2+Oxixh8cT6eKnUgMG0dkomFfdr1jze20zVXpVK68m/331+Jo6cj01tP5/WgVHic+HyHnZ0Pv+IF8I3kJ8KnoxOWHiQVG+jlvIpC/FnxhKpmGIIRg1K5RusofAxfptEKLX7Af049PJygmiAaeDVjUaZHstIketVbN1CNTWXhmIS3KtGDbgG1G1aAHxwTT5tc2mCvNOfXeKaNSRHoS0xNptKIRSZlJXP3wKu627kbbLIyRO0ey5uoarnx4xWR/j68Lb5x7Lp6kPqHakmpUdq7MqfdOGZVK0ZOuTqfV6lbciLnB6fdPU8ejjlH2Vl1Zxehdo1FqyuGa8RVmFD4fVALuze+eb7olIDKALw58wbH7xzDTulNC/Q42mrZIOapgJfJXeNQPEtHbz2ubnAqPBZF7KMm07YHZ2u9KSWJQk9J808c0f+j6ISCFkanJZNP1Tcw/PZ8bMTeo6lyVmW1m0r9Gf6Oj14ikCAZvHcyJByf4qMFH/Nj1R9mLsKBz7O3WtkMIwYkRJ6jqIn8soh6t0NJnYx/23t7L0eFHs2f/FifH7x+n7a9tmeQziQUdi7/U8lXjjXPPg/XX1jPUb6hJc4oRSRE0WdkEIQRnPzhrtODRvtv76PH720jCCteMKViIgqf/5DfFKSdCCPbf2U//DZ+RIm6j1Lpjr+6DraYDCqzwcrAi4q9ux9zobx56CltsLYictoozcjeEqOQoVl5eyf/8/0dEUgQ1XGswpeUUBtYYaJIb/66QXby/832dXG73n3m3zrtG2QuIDMgWJjs2/JjBEsSFMeXIFOadmsdPXX5iXJPir45JyUyhzjJdEHTt42tYq6yL/ZivGoY691e6FDI3g2sNplfVXkw5MoWg6CCT2CxpV5I9g/eQlJlE53WdZdet6+lauSvft9mFAnMiLSbzVLkLgUCllFApnk3V6EsZCxt8IUkSXSt35bceRymlmYmZcCLefDmPLEfw1GIF7/goCqyDH71rNPWX1+fLA18apdyY8xhFGRZuKtRate4mt6U/pReXZtqxadRwrcHewXsJ/DiQwbUGG+3YE9MTGblzJL029qKUfSkujb5ktGM/9fAUbX5tg4WZBSdGnDCZY199ZTXzTs1jdP3RJqkkM4TJhycTGh/Kyl4rTerYX/bwl38i/9rI3dCyvtxEJUdRe1lt3GzcuDDygsk64k7cP0GX9V3wdvHmyLtHZEm+5uS389f57OBI4rXncVK0YHHH/3ErkufSGA3LOhUpAtanQlIJJkm1izSz02iFmiqO9Ul+0glVZotn7MztWxNz2wBuxNxgw/UNWMV/x6OEFKQccYGWDBJVa0lX3MRCWxnHrJHZaR8t6QgysVU5PnNO5SfvMehJwVi0QsvZsLNsDtrM5hubiUyOxNnKmWG1h/FRw49MktrQs/vWbj7e8zERSRFM8pnEjDYzjC7v23pjK0O2DaGcQzkODD1gkhw7wP47++m5oSdtyrVh7+C9RSrDlcvB0IN0XteZz5p8xg9dfjCZ3Zf9FPiiMWnkLklSF0mSQiRJuiNJ0uQCtusnSZKQJKnQAxtDfsJJhtyt3W3d+bXPr1yPvs64faZ7DG1drjV+A/0Iigmi/dr2xKbGGmVvWJOaPJl2hkWdFpHEeT4/3oFfL2/LrlrRCMHWS+HM2BlkcAS8/Uo4Wy+FoxECC1ENl8yJVMj6jeHVp2GuysSnWupzIwD71i9F9yrdqepSFS97r+eaoQSZZJofoZRLBt4WE5FQorA9yNCmZXArkUGCag0xVl+gdpmMh2tY9n4uJdJIUu4mTeGPhuTs100h+5uUkcSOmzsYvWs0JReVpMXqFiy/tByf0j5sHbCV8PHhLO6y2GSO/WHiQ/pt7kfPDT0pYVGCsx+cZV6HeUY5diEEC08vpN+WftT3rM+p902zeApw7tE53t78NjVca7B1wNYX4tijU6IZvn041V2rM6/9PJPafhlPgf8GCl1xkiRJCSwFOgKPgIuSJO0UQtzItZ0d8ClwvjhONCcFfZiG3Km7VOrClBZTmHtqLk1LNZU9Qi8vuzve2UGfjX1ovaY1B4cdpKRdSdn2FJKC8c3G0758e3x+6Uu8cgbWqtY4ZY1EiSNpWZp8K1TySp/k9b5lZdlxO7Qt1/5vFlnarHwX/G7H3sbDxoM+9bzQCA2LDtzmcWI6JewjcS+ZwLS2/6FV2VZsCbJn5ZWVfNOnFiW9TrL7loa9QyL548YfTD8+nQNDDxAaF4qT53ZC7oWRKi5grg3GUT0MS5Ui32HhBZGYnsj58POcfHCSY/ePcT78PGqtGnsLezpX7Ezfan3pXqW77LLK/EjNSuW7M98x/9R8AOa0m8MEnwlGLZoCpGWl8eHuD/nt2m8MrDGQ1b1Xm+wJMyAygK7ru2aXZJr6PckLrdAyzG8Y8WnxHBx60OT6MQWNG3ydMUQ4rDFwRwhxF0CSpI1Ab+BGru1mAwuBCSY9wzwwxYc5q+0s/B/788neT/B28TZ4lFphdKnUhX1D9tFrYy98fH3YN2Sf0TnSOh51cE39ngSzLSSabSZN6Y9D1lDsNN2QyDtHnFcEXJBAlyRJmCvN8013RSRFUMpe1wHZp64XfeuVQiEp2Hh9Iyfu2+PtorvGdHU6FRwqcDv2Ng8TH2Zrk7tau1LSriQJ6Qkcv38clXkCa/v8zuz9x7iZtgxH+ximd+1Y4M1ZCEFUShRB0UEERgdyJfIK/hH+BMcEIxAoJSX1PeszodkEOlfqjE9pH6MdbV6otWrWBqzl62NfE54UTr/q/fiu43cmiazvxd/j7c1vcyXyCrPazGJaq2kmqwEPjAqkw28dsDO34/C7hguVGcucP+dwMPQgy7ovK5ayx/wqvYpj+Mu/CUOcuxcQluP/j4BnNEAlSaoHlBZC7JYkqdiduyk+TKVCyYa3N9B0ZVP6bOrDuQ/OUdGpoknOr235thwffpzuv3fHZ5UP2wZsK5KWSV54OdhDwmBsNK2IUy0j3nw5ydp9lFKMxFzd8JlpSPlpxuQ3uFov0JU7d5lTrjc8KZzqrtUBXYOSEAKFpOBx0mMcrRyzUxAxqTF42XtxP+E+Gq3mmYlCzlbOBMcEE/Y0DJ/SPvSp50XjSu346fx1arqZ0ae2F0IIJEni0dNHbAnawqOnj3j49CF34+9yJ+4OTzOeZtvztPWkvmd9BtYYSLNSzWhaqil2FnZGvc8FodFq2By0mZknZhISG0Jjr8ZseHsDLcsWbfzc2bCzlHcsn6dzXXxuMXfj77Jr0C56VOlhqlMnIDKA9mvbY2lmydHhRw2a9GQK9t3ex/Tj0xlaeyijG4wulmPk16Mh5ynwVcIQ555X2JDtISRJUgCLgRGFGpKk0cBogDJl5GuymOrDdLJy0gk3+Taj6/qunH7/tEmGHAA0KNmAsx+cpceGHnRa14kfOv/AmEZjZEdh+msmqxRumbNJU5wjwXw19/ia6m5NsE16h5SnlQtcXM6vy1T/ekHpLtdy6dkCVznrxy3MLHRyAup07C3sCY4JppFXI5QKJVqhzX7sT0hPQCkpEQji0+LxKe0D6BQd49Pin4uwHyY+ZPzB8ViZWVGmRBnKOZSjWalmVHWuSnXX6tR0q/lCmm1AVwv/e+DvLDi9gJtPblLDtQbbBmyjT7U+Rfo8A6MC6b+lP+627jhaOjKm0Rg6Vez0zDbzO8zni6ZfUN6xvMnO/9yjc3Rd3xVbc1uODT8mewxgUbkVe4tBWwdR2722SaSI80P/XZdTYPEqY4hzfwTkLN4uBeSc0GwH1ASO//XheQA7JUnqJYR4phxGCPEL8AvoqmXknrQpP8wqzlXYNWgXHdZ2oOv6rhwdftRkecjyjuU5+8FZhmwbwth9Y7kYcZGl3ZbKUr/Lfc2V7dvxRceRRGv3MvvP2URmfUEb7zZMaTGFDhXyzvN7FdCoBHmntRLNthGRdhB1SDhxaXHMaDMDV2tXrFRWVHKqRNtybZlwaEJ2Kd3lyMsMqT2E2u61+eHcD6gUusW6kNgQbMxtqOBYgQeJD+jr3RfQ1T2nZKXgZae7Pr0DaFiyIbGTYnG0dHxprelxaXGsvLySn87/RHhSOHXc67C532berv62rAanC+EXGFl/JBN8JrDqyiq2BG0hLSuN3tV6Zz+xWKusTerYD4Ye5K1Nb+Fh68Hhdw+/sIg9Pi2enht6olKq2P7O9mKvZ+9Tz+u1d+a5McS5XwQqS5JUHggH3gGyhzwKIRLh71ZKSZKOAxNyO3ZTY8oP06e0D38M+IPeG3vTbX039g/dj625rUls21vYs+OdHcw+MZuZJ2ZyMeIim/ptoqZbzSLbyvuax/Be3fdYfmk53575lk7rOlHHvQ5fNP2CgTUHPiMoVdgTT17pLnt1LyrYtOXHIeUIjglGpVARnhRObGospe1L4+3qTQ3XGnRY2wFzpTl9q/WlUclG2JjbkJyZzM0nN6nmUo1119axuPNiPGw9eJD4AAulLo1zJuwMtua2z+WrzZXmOFk5Ffk9MgWXIi6xzH8Z6wPXk6ZOo3359qzouYIulboU6UazLXgbtua2NCvVDDsLO44/OE4FhwoA9K3WV6ftH7ie3tV6F8sNbG3AWj7Y+QE1XGuwf+j+F5Zjz1Bn8Nbmt7gXf48j7x55YTeUN+RCCFHoD9ANuAWEAlP/em0W0CuPbY8DDQuz2aBBA/FPY0vQFqGcqRStVrcSSRlJJrd/KPSQcPvWTVh+Yyl+OPuD0Gg1JrWfnpUufC/7iupLqwtmIFwWuoiJByeKW09uZW/jd/mR8Jl3RJT7v93CZ94R4Xf50TO/qzZtnyj7f7uzf6pN2/fMNnmRpckSt2Nvi5MPTor0rPTs18+FnRONVzQWFX6sIBafXSyyNFlCCCGWXVwmhvsNF2uvrhXtf20v9t7aK7RarUnfi6ISnRwtfjz3o6i7rK5gBsJ6jrUYuWOkCIgMKLKtpIwkMXDLQNHol0binT/eEW9velukZKaIkw9OiharWmRvdyf2jhi6bajYHbJbCCFM9h5otVrx9dGvBTMQ7X5tJxLSEkxi1xA0Wo0YsnWIYAZi7dW1L+y4rxOAvzDEbxuyUXH8/BOduxBCbAzcKJQzlaLZymYiPi3e5PYjkyJF9/XdBTMQbde0FaFxoSY/hlarFYdDD4u+G/sK5UylYAaiuW9zsdx/uYhNjS1w34Kcv7HnpCctK03MPjFbDN02VPx88WeT2JdDQlqCWHt1rei2vpswm2UmmIGov7y+WHphqazPPio5SgghxNXHV0WbNW2yXx+3d5yYd3KeuBZ5TYzaOUr4XvYVQggRkxIjZhybIX4L+M0k1+N3+ZFoMnePsJ7WUufYfQeIDHWGSWwbglarFV8e+FIwAzHnzzkv7LivG2+cuxFsvbFVqGapRJ2f64jHSY9Nbl+r1YoVl1YIu7l2wuobK/Ht6W9FpjrT5McRQojwp+Fi3sl5otqSaoIZCNUslei6rqvwvewropOji+WY/2TCEsPEsovLRNd1XYVqlkowA1FmcRkx6eAkERgVKMvm79d+F+1+bSemHZkmhBAiPi1etFnTRgTHBAshhDhy94iYcGCC2BK0Rey9tVc0XtE4+6ntXb93xdYbW4UQxkXufpcfiQrT1gjzrysKpkvCYeoIUXXaXpPdnA1hzp9zBDMQY/eMfelPYq8yhjr3f638QHGjX4hytXFl35B9VHMpWMBLDmGJYXyy9xN23dpFLbdaLOm2pNhU+YQQXIm8wobADfwR/Af3E+4jIdG0VFO6VupKp4qdaFCygUFKiv8mkjOTOfXwFEfuHuFA6AECo3WlnRUcK9C3Wl/e9n6bJqWayFaAPPngJF8d+4rJLSbTpZJu7N/d+Lss919OLfdaDK09lExNJt+e/hZLM0u+9PmSfpv74WLtgoXSgpMPT/Lfrv81us+i+tz5hGTORaDFNXMCVtpGgGHCcqbgp/M/8dn+zxhSawhr+64tdj3415k3qpAm4GL4RXps6EGWJoutA7YaXaueF0IItt/czucHPudh4kP6V+/Pgg4LTFoxkdcxr0ZeZUfIDvbc3sOliEsIBCUsStCiTAtalW2FT2kfGng2+FdNoxdCEJ4UzvlH5zn76CynHp7i0uNLqLVqzJXmNC/dnK6VutK9Sne8XbxNsog5/dh0rFRWTG4xmQx1BgpJgZnCjP9e+C+Pkx7zYcMPKedQjrUBa9l+czvbBm4jNjWWK5FX2Hd7H581/cyoUY1ZmiymH5/OvFPzUGnL4Zo5BZX4u1rK1Fo9eaGfJta3Wl8299/8ygUI/zTeOHcTcS/+Hj029OBW7C1+6vITHzX8qFgqG1KzUll4eiELTy9ErVXzSaNPmNJyisnq7gsiJiWGo/eOcuTeEU48OMGt2FuArp69pltN6nvUp45HHWq51aK6a3XcbNxe+uSctKw0bsXeIigmiOvR17kaeZUrkVeITI4EwEJpQSOvRrQs05I25drQokwLo8vxNFoNSoUyu2wR4MdzP+Jg6cDTjKf4XvGltnttulfuTm332qy7tg6BYG77udx8cpPJhyezsd9Gk4zEA913c8i2IZx9dBY3RTcsUt5HwbO2iztyX3phKWP3jaVnlZ78MeCPYukIfsOzvHHuJiQxPZHB2waz9/Ze3q/7Pku6LSm2iDb8aTjTj09n9dXVWJlZ8WmTTxnfbDwu1oUP7jAV0SnRnHt0jvOPzuP/2J/Ljy9nD6cGcLB0oJJTJSo6VqScQznKlCiDl50XnnaeuNm44WLtgo3KRvYNIF2dTmxqLDGpMUQmRxKRFEFYYhgPEx9yL+EeofGhPEx8mL29mcIMbxdv6nvWp4FnAxp7NaauR12TDVxed20dO0N2UtejLuObjX/GOc89OZfQuFAszCx0khYR/sw9OZcl3ZZgb2FPn419qONRhz239jC/w3yT6BgJIVgbsJZx+8YhSRLLui/DSt3qhSsj6sdD9q7am039Nr0ZcP2CeOPcTYxGq2H68enMOTmHuh512dxvM5WdKxfb8W4+ucnMEzPZdH0T1iprRjcYzfhm47P1XV4kQggikyMJjA4kOCaYkNgQ7sTd4W78XR4kPkCtfX50n5nCDAdLB+zM7bAxt8HSzBJzpTlKSZnt9DVaDZmaTNLV6aRmpZKcmUxiRiLp6vQ8z8PD1oNyDuWo6FiRyk6V8Xb1xtvFm6ouVYstYrwQfoHP9n/G9NbT+eXSL1R1rkq/6v1oULIBoMuvj9g+ghquNfi5x88A9NrQi5ZlWjKx+UTCEsMIjA6kumt1k9R7P056zEd7PmJnyE5alW3Fr31+zbYrVwa7qAgh+PrY13xz8hsG1BjAur7rXoiy5Bt0vPLO/UV9kXOz+9Zuhm8fTqYmk6XdljKs9rBiTVHciLnBvFPz2BC4AUmSeKfmO3ze5PNs5/Ky0QotUclRhCeFE5kcSXRKNLGpscSlxZGYkUhSZhIpmSmkq9PJ1GSiEZrstIZSUqJSqrA0s8RaZY2tyhZ7C3scrRxxtnLG1cYVdxt3StqVpKRdyZcSGc46MYuE9AS+7/w9oXGhbA3eSmxq7DPj4RaeXsiT1Cf0qtqLFmVaMHLnyGwlSlMhhODXgF8Zf2A8aeo0vmn7DZ83/dwkU6OKgkar4ZO9n7D80nI+qPcBy3ssf+Hn8LrzSjv3ly3OH5YYxpBtQzj58CQDagzg5+4/F3s35f2E+/xw7gd8r/iSnJlM01JN+bjhx/Sr3s/kE23eaHT8zaHQQyy5uAS/gX4oJAXH7x9n0/VN9K/Rn3bldbnsuLQ4jt07xu/Xf+dO3B3qedRjSbclJutyvhV7izF7xnDk3hGal26Oby9fkw4ZMZTUrFQGbx3MjpAdTG4+mbnt5770tZfXkVfauec3x/NFlX2BLoJZcHoB049Px8XaheU9ltOraq9iP25ieiIWxeWfAAAZgElEQVRrrq7hZ/+fCYkNoYRFCQbVHMSIuiNo7NXYqD+2l33T/CdyL/4e80/Np0eVHvSs2pPHSY9Zc3UN7rbuvF/vfTRaDVqhRaVUEfIkhBKWJUzW5p+alcq8k/NYeGYhlmaWzG8/nw8bfvhSygwjkyPptaEX/hH+/NT1pxc2lu8Nz/NKz1DNKXCVoQhGoH3u9eJGqVAypeUULo66iJuNG7039mbgHwOzqzWKixKWJfis6WcEfxLMseHH6FGlB2sC1tDUtylVl1Rl+rHp3IjJLbVvGG8m2ujSTDkpXaI0tdxrsef2HjRaDZ52njx6+oikjCTuxd9j1olZhD3VKWJXdalqEscuhGDj9Y1UW1KNb05+Q//q/QkZG8LHjT5+KY49IDKAJiubEBQThN9AvzeO/V/Cv9K563XbM6V7RJr/H7GqxQg0L0Wcv65HXS6OusjstrPZfnM71ZZUY+mFpWi0eU9IMhWSJNGmXBvWvbWOyC8j8e3lS+kSpZn952xq/K8G3ku9mXJkCucfnX/OYeXH6zrR5l78Pf538X90Xd+VJiufGVWAmcKM3lV7k5iRyKwTswBIVafiaOVIecfyfNrkUyo4VjDZuZwJO0PzVc0ZtHUQztbO/DniT9a9te6FiX7lZuuNrfis8kGj1XDyvZP0rtb7pZzHG4rOvzIto08fpGapeWq2mQTVb9hoG+PbYz0DG70Yreq8CHkSwpi9Yzh67yj1POrxU9efaFGmReE7mpDHSY/ZGrwVv5t+nLh/Ao3Q4GrtSpdKXehcsTPtK7TP11H8E9JdL4L4tHhOPDjB4buHORh6kNtxtwGo5FSJXlV6saDjgucacW7F3mLWiVlcibxCTbeaJl9nuRFzg6lHp7L95nY8bT2Z3XY2I+qOeGmLlRqthq+PfZ09inLbgG142nm+lHN5w7O80jl3eHbhT2F3mHvqH2ns1Zhdg3a9kMaf/BBCsDloMxMOTeDR00f0q96P+e3nm2zKU1GIS4tj3+197L2zlwN3DhCbphva7e3ind3Y07x0c8qUKIMkSa9kzl0Iwf2E+5x9dJYzYWc4+fAkgVGBCATWKmtal21N54qd6Vq5K1WcqxRoK0uTRVJmkkmd+u3Y28z+czbrA9djo7Jhos9Evmj2hckWY+UQkxLD4G2DOXz3MCPrjWRJtyVvatj/Qbzyzj03fsF+DN42GC87L3YP3l0sWjBFISUzhe/OfMfCMwvJ1GTyYYMPmdZq2kt7vNYKLVceX+Hw3cMcf3CcUw9PkZyZDOjG1TXyakRDz4akp5bhwFULniTa4uVgXazVMqauzNFoNYTGh3It6hpXI69y+fFl/CP8iUmNAcBGZUOz0s1oVaYVbcq1oUmpJi+to/Lmk5vMPTmX9YHrsVBa8EmjT/i/Fv+Hi7XLS61Y+vPBnwzaOojY1FiWdlvKB/U/eCHHfYPhvHbOHeD8o/P02tiLDHUGm/ptonOlzia1L4fHSY+ZeWImKy+vxFxpzieNPmFi84m42bi91PNSa9UERgVyJuwM58LPcTH8IrdibyH+mqDoYOlAddfquiYh56pUdq5MBccKlHMoZ5JJVXKfEvR19fcS7hEaF8qduDvcirvFzSc3ufnkZnYDlFJSUt21Og1LNqRRyUY0LdWUWu61XrruyYXwCyw4vQC/YD+sVFZ81OAjJjafmH3Tf1lPTxqthjkn5zDzxEwqOFZgS/8t1PWoW2zHe4N8XkvnDvAg4QG9N/YmMDqQee3nMdFn4j+iFvdO3B1mnZiVHamNbjCaL5t9SekSpQvf+QWRlJFEQFQA16KuERgVSFBMEDef3MyOfPU4WDpQyr4UXnZeeNh64Gbjhqu1K87WzjhYOmBvYY+9hT02Kl1nqoWZBSqFCjOFGQpJgUDQ5YfjRCSmgKRGkIkgA62UhpONlmm9yhKfFk9sWiwxKTFEpUTxOPkx4U/DCU8KJ1OTmX0uEhJlHcpSzaUa1V10s1VrudeihmuNf4zomUarYWfIThafW8zJhydxsHTgk0af8FmTz55LIb6MdY/7Cfd51+9dTj48yZBaQ/i5+8/FOmj8Dcbx2jp30Mm8vr/jfbbc2EK/6v3w7eVrsrmoxnIr9hZzT85l3bV1SJLE4FqDGd90PHU86rzsU8uXhPSEbLmBe/H3CHsaxqOnj4hIiiAyOZKolKhnHK4pcbB0wN3GHU87TzxtPSltX5oyJcpQ3rE8FRwrUN6h/D82HxybGsvqq6tZenEp9xPuU7ZEWT5r8hkj64/M13mWn7yHvP4ii0PdUd/1+um+TwF0Hdd1hpn0GG8wPa+1cwfdF3fR2UVMPjwZb1dvLo++/I/Sv3iQ8IDvz36P7xVfUrJSaFOuDZ82/pSeVXu+9NRBURFCkJyZTFxaHPHp8TzNeEpSRhKpWamkqdPIUGc8Iz0A8OORUBJTNUiYIWGOJCyQsMLd1oHNo9vjaOmIk5XTP+ozMwQhBKcenmLF5RVsDtpMhiaDlmVa8mmTT+lTrU+hn+2LitwjkiL4aPdH7Lq16zmNmjf8s3ntnbuekw9OcifuDu/Vey/P3x2+e5gLEReY137eS8kxxqfFs+LyCpZeXMrDxId42Xkxqv4o3q/3/j8qZWNqXrXKnEdPH/FbwG/8f3v3HhV1ue9x/P3lKiJyCUEUQVRSvKab1ERE8ZquLeaxc+x6LE8tK8uOxTpZq3J5dtlu723tVlrbSq12VkczI/NWqWUZKqZZSoB3QA1EEAUGBnjOH7+REFF+tof5DfS81nKtGebH8HEYHh6ey/dZ8cMKsouyae/bnjv73cms+Fn0C+9n+nma+3VRSrF833Ie2/wYtmobzyc/z5yhc/ThGi2IUxt3EZkA/B3wBN5USr3Q4PG5wH8B1UAhcK9S6vjVntPqqpA/nP6Bu9fezdyhc7FV2/go8yPe+OMbRAdFW5KnuraaddnreC3jNTYf3owgjOs+jhk3zCClZ4rbjB87U0uvY1NcUcyazDWs/GklW49uRaFIjErk3oH3cmvvW/H38f9Nz9tcr0tOUQ6zPpvFlqNbSIxK5K3JbzVrZVOteTitcRcRTyAbGAvkAbuB25RSB+tdMwrYqZQqF5EHgJFKqf+42vNa2bgXlhWy6LtF+Hr5Mn/kfAAG/WMQH0z7gOuvu/6SwxiscLT4KMv3LWfFvhXkluYS4BPA1Lip3Nb3NpJjklvcUEVrcrbiLGlZaaw+uJrNhzdjr7XTI6QHd/S7g7v632XJfoamVNgrePHbF1n4zUKjRs2YF7j/D/fr3noLZbZxNzO4Oxg4pJQ64njiD4AUoK5xV0ptrXd9OnDntcV1re0ntlNYXsgzSc8AxvK0myJvwlOM3YAXG/bMwkziOsS5PF9McAwLRi1g/sj5bDu2jX/u/ycfZX7E2z+8TYhfCFN6TmFq3FRGdxt9zaf6tPTeshWOFB/h06xPSctOq9v1GxUYxcODH2Z63+nEd4p3ixVZDSmlWJe9jkc3PcqR4iNM7zudReMW6Z2mvxNmGvfOQG69+3nAkCtcCzAT2NDYAyJyP3A/QFTUbz838l+17dg24kLjiAqMwlZtI+uMURir/q7AI8VHePP7N/n8yOekDku1ZBWBh3iQHJNMckwySyYtYdOhTaw6uIrVmatZtm8Zbb3bMrbbWCbFTmJCjwlNjtE3HM/NL6lg3hrjwGjdwP+qrKqM7Se2s+nQJjYc2kBWkfH+iAuNI3VYKlPjprptg35RZmEmczfPZeOhjcSFxvHFXV8wuttoq2NpLmSmcW/sHdzoWI6I3AnEA0mNPa6UWgosBWNYxmRGp6qwV/BZzmd8c883AOw5uYe9p/cyKGIQ4e3C64ZkwvzD+Nv4v7H/l/08tP4hbNU27vvDfVZEBqCNVxtSeqWQ0iuFqpoqth7dyidZn7Auex2fZH0CQO8OvRnbbSyjuo4iqWsSQW2CLnmOq1V9/D037hX2Cnbm7+SrY1+x9dhWduTuwF5rx9fTl5FdR/JA/ANMun4SPUKsq1tkVkFZAfO3zWfpnqW082nHonGLmD14th7K+x0y07jnAfW7hJHAyYYXicgY4CkgSSlV6Zx4zufl4cWorqNYn7OehKgEXkp/iRs63sDUuKmXXHexF98/vD+zb5zNvtP7sNfY8fb0tnxM3sfTh/E9xjO+x3gWT1zMgcIDbDy0kc+PfM7SPUv5+86/IwgDOg5geJfhJEQlMDRyKPkl5TT2u7q1V32sTylFbmkuu/J3kZ6Xzo7cHew5tYeqmioEYWDEQOYMmcOYbmMYET2ixUxkX6i6wKLvFvGXHX+hwl7BrPhZzB8536Vn72ruxcyEqhfGhOpoIB9jQvV2pdSBetcMBFYDE5RSOWa+sJUTqrvzd/PIxke4zu86JveczL0D78XLw4taVXvZJFN2UTaLdy3GQzx4acJLnL5wmvd/fJ/MM5mkDkt1u9UGldWV7MzfydajW/n6xNfszNtJmb0MAG+C8KqJxae2Bz613fFRMXiqMCKD2raqqo8XNaw1s/f0XjJOZlBQVgCAr6cv8Z3iSeiSQGJ0IsOjhl/21467s1Xb+EfGP3j+m+cpKCvgll63sHD0QktOatJcw9lLIScCL2MshVymlHpORBYAGUqpNBH5AugHnHJ8ygml1FWPJbJ6KSQYS9mC/YJ5PeN1JvecTKeATnWPZZzMID0vnVUHVzG081DmJc7j9IXTPPnlk3QO6Ezn9p1Zl72O9//tfbdej15dW83+X/aTnpfO6h+38e2JnVSRB2LUePdQfvQIiWN49A30Cu1Fz9CexIbEEhMcc82TtVYpsZVw+Oxhcs7mkF2UTVZRFpmFmWSeybyk1kxchzgGRQzixk43MrjzYAaED3Db3a1NsVXbeOv7t1j4zULyz+eTHJPMc8nPMTRyqNXRWoyWurhAb2K6BtuPbyciIIJw/3A2HNrAqoOrKLGVkNAlgYQuCYztPpZT50+xePdifDx9eHrE04gISSuSeHrE04zpNsbq/4Jpa/fm88LGfRwv/Zm27fLoGVlMBcc5WHiwrkcLRs2WiIAIogOjiQ6KJjIgks7tOxPRLoLwduGE+YcR2jaUEL+QZtlRq5Si3F5OUUURBWUFFJYVcvrC6boaM7mlueSW5nKs5BgltpJLPjcqMIreHXrX1ZrpH96fPmF9Wswvq6spqyrjze/f5MUdL3Ly/EkSuiSwYNSCuvNcNXNa8iY6Zy6FbPUSoxMBo9xp6uepeIgH+2ftv6T+xxdHvqDCXkFKzxREhAMFBwhtG0q/MGP34Yc/fcimw5voG9aXuTfNteT/YcaUgZ0db97L65QUVxSTXZRNztkco45MyVGOlxxnd/5uPi79mMqaxqdSAnwCCGwTSIBPAAG+AbT1bouflx++Xr74ePrg7eGNh3jUFQ2rVbXU1NZgr7VTWV2JrdpGub2cMnsZ5yvPc67yHOds57DX2hv9esFtgolsH0lUYBTDIofV1ZmJDYmle0h3px4Y7i6KyotYsnsJr+x6hTPlZ0iKTuKdKe+QHJPs1qt23NXvYXGBbtzrGRE9goMPHuRPX/+JUW+PYkqvKcwbPg8R4eT5k0QEGHXPwTgOred1PbFV2/jrjr+SlpXG48Me57WM17hQdaFuDX1LEuwXzJDIIQyJvHylq1KKYlsxp86f4peyXygoK+BM+RmjnkxFMecqz1FaWcqFqguU28spLC/EVm3DXmPHXmunVtVSq2oRBA/xwNPDE28Pb3y9fGnj1Ya23m0J8QshwDeA9j7tCWoTRLCfUV+mQ9sOhPmHEd4unIh2ES1mktMZDp89zMvpL7Ns3zLK7eVMjJ3IvOHzXH7CV2vjyiMlrRr+0Y17A/4+/iwcs5AHzz3Iez++V3fM2cc/f8yzSc8CxvLJnLM5dA/uzi9lv5CWlcarE1+lf3h/yu3lfHPCWGZp9aoaZxIRQvxCCPELoQ99rI7Tqiml2HJ0C6/seoVPsz7Fy8OL2/vdzuPDHqdvWF+r47UKnYL8Gi3Q5uxzmK3cW6L3H19Bl8AuPDH8CcAY5xzYcWDd2O6CrxcQ1CaIEdEj+DTLqKrXP7w/tmobnuJJoG8gtmpbq2nYNdcosZXw6q5X6bOkD2PeHcOO3B08mfgkxx49xoopK3TD7kSp43vi533p+bR+3p6kjnfuKqOrDf80N91zN8Hfx58ZN8zg7rV3896P7xHuH86TiU9yvOQ4n2R9wua7NgNQWllKel46Hfw7tIrJO615rd2bz4sbf+bo+b3U+n3JOfmKypoK4jvFszxlOdP7Ttfvo2Zysdfc3MMlrhz+aUg37iYNiRxC1uwsTp0/VbcxZE3mGgZ0HEDHdh0prSwl42QGWUVZpCakWpxWc3fLvtvDExuWUCKfY/fNRWra0F6N5LmRj/DYqJutjve78OvigubjquGfxuhhmWsUERBRt5V7ZNeRdZOI7+1/j3XZ65jSawod23WkVhnryJVSPL/9eX4q+MnK2JobOF95nnd+eIdx745j5ubBFHouw0O1I6TqYSJt7xBUOZs1Oy9dd792bz4JL2wh5onPSHhhC2v35luUXvstXDX80xjdc/8X9A/vT3RgNInLE4kNiWX24NkkdEkAqNvpmlWUxbPbnuWpLU8xKGIQd/S7g+l9p1+yYUprvcqqylifs54PD3zIZzmfYau2ERMUQ6D9VvxrkvFWl/Yc6/+5rgu9tXyuGv5pjN7E5ATnbOeoVbUE+wU3+nhhWSErf1zJu/vfZc+pPQhCUtckXpv0Gr1Ce7k4reYKJbYSZqbNZEPOBiqqKwj3D2da72nc3u92boq8ieF/3trkcXpWHJatuT+9icmFAtsEcrVfkh38OzBn6BzmDJ1D1pksVv64kjU/ryHMP8yFKTVXCvQNJL80n3tuuIdpvacxInpE3bJaMP5cb2yHZP0/162cjNNaPt1z1zSLNLW5RffctcbonrumubmmVmuY6d1r2pXoxl3T3JSVk3Fay6cbd01zY65Yi621Tnqdu6ZpWiukG3dN07RWSDfumqZprZBu3DVN01ohU427iEwQkSwROSQiTzTyuK+IfOh4fKeIdHV2UE3TNM28Jht3EfEEFgM3A72B20Skd4PLZgLFSqkewEvAn50dVNM0TTPPTM99MHBIKXVEKVUFfACkNLgmBXjbcXs1MFr0SRWapmmWMdO4dwZy693Pc3ys0WuUUtXAOeA6ZwTUNE3Trp2ZTUyN9cAbFqQxcw0icj9wv+PuBRG5lrOmQoEz13C9FXRG59AZnUNndA53yxht5iIzjXse0KXe/Ujg5BWuyRMRLyAQONvwiZRSS4GlZoI1JCIZZorlWElndA6d0Tl0RudoCRkbY2ZYZjcQKyIxIuIDTAfSGlyTBvyn4/Y0YIuyqtykpmma1nTPXSlVLSKzgU2AJ7BMKXVARBYAGUqpNOAt4F0ROYTRY5/enKE1TdO0qzNVOEwptR5Y3+Bjz9S7bQNudW60y/ym4RwX0xmdQ2d0Dp3ROVpCxstYdliHpmma1nx0+QFN07RWyO0a95ZQ6sBExrkiclBE9ovIlyJiaumSKzPWu26aiCgRcflqADMZReTfHa/lARFZ6W4ZRSRKRLaKyF7H93uii/MtE5ECEfnpCo+LiLziyL9fRAa5Mp/JjHc4su0XkR0iMsDdMta77kYRqRGRaa7K9psppdzmH8aE7WGgG+AD/AD0bnDNg8DrjtvTgQ/dMOMooK3j9gPumNFxXQDwNZAOxLtbRiAW2AsEO+6HuWHGpcADjtu9gWMuzjgCGAT8dIXHJwIbMPaiDAV2ujKfyYzD6n2Pb3bHjPXeD1sw5h+nuTrjtf5zt557Syh10GRGpdRWpVS54246xt4AVzLzOgL8L/AiYHNlOAczGe8DFiuligGUUgVumFEB7R23A7l8D0izUkp9TSN7SupJAd5RhnQgSEQiXJPO0FRGpdSOi99jrPl5MfM6AjwMfAS4+n34m7hb494SSh2YyVjfTIyekys1mVFEBgJdlFLrXBmsHjOv4/XA9SLyrYiki8gEl6UzmMk4H7hTRPIwenQPuyaaadf6frWaFT8vTRKRzsAtwOtWZzHL3c5QdVqpg2Zk+uuLyJ1APJDUrIka+dKNfKwuo4h4YFTvnOGqQI0w8zp6YQzNjMTozW0Xkb5KqZJmznaRmYy3ASuUUn8TkZsw9nv0VUrVNn88U6z+eTFNREZhNO7Drc7SiJeB/1FK1bSUmoju1rg7rdRBMzKTEREZAzwFJCmlKl2U7aKmMgYAfYFtjjdqRyBNRCYrpTLcJOPFa9KVUnbgqKMWUSzGrmlXMJNxJjABQCn1nYi0wahF4i5/upt6v1pNRPoDbwI3K6WKrM7TiHjgA8fPSygwUUSqlVJrrY11FVYP+jeYsPACjgAx/DqB1afBNQ9x6YTq/7lhxoEYE3Gx7vo6Nrh+G66fUDXzOk4A3nbcDsUYXrjOzTJuAGY4bsdhNJzi4teyK1eerJzEpROquyx6T14tYxRwCBhmRTYzGRtct4IWMKHqVj131QJKHZjM+BegHbDK8Zv+hFJqsptltJTJjJuAcSJyEKgBUpULe3UmMz4GvCEi/40x3DFDOVoAVxCR9zGGrUId4/7PAt6O/K9jzANMxGg8y4F7XJXtGjI+gzFvtsTx81KtXFyoy0TGFkfvUNU0TWuF3G21jKZpmuYEunHXNE1rhXTjrmma1grpxl3TNK0V0o27pmlaK6Qbd03TtFZIN+6apmmtkG7cNU3TWqH/B0Bzx3uZ+thuAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#画高斯图的等高线\n",
    "plot_contourf(data,lambda x:gaussian_nd(x,u,sigma),8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 二.高斯混合模型\n",
    "高斯混合模型模型定义与第一节类似，可以定义如下：   \n",
    "\n",
    "$$\n",
    "P(X\\mid\\theta)=\\sum_{k=1}^K\\alpha_k N(X\\mid u_k,\\Sigma_k)\\\\\n",
    "\\alpha_k\\geq 0,\\sum_{k=1}^K\\alpha_k=1\\\\\n",
    "\\theta=\\{\\alpha_1,\\alpha_2,...,\\alpha_K,u_1,u_2,...,u_K,\\Sigma_1,\\Sigma_2,...,\\Sigma_K\\}\n",
    "$$  \n",
    "\n",
    "\n",
    "这里$K$表示高斯混合模型中高斯模型的数量，$\\alpha_k$表示第$k$个高斯模型的权重，由于有$\\sum_{k=1}^K\\alpha_k=1$的约束，所以$\\theta$的自由度还可以少1，比如去掉$\\alpha_K$，类似于第一节，我们可以人为的求一组高斯混合模型..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "D:\\ProgramData\\Anaconda3\\lib\\site-packages\\sklearn\\utils\\deprecation.py:144: FutureWarning: The sklearn.datasets.samples_generator module is  deprecated in version 0.22 and will be removed in version 0.24. The corresponding classes / functions should instead be imported from sklearn.datasets. Anything that cannot be imported from sklearn.datasets is now part of the private API.\n",
      "  warnings.warn(message, FutureWarning)\n"
     ]
    }
   ],
   "source": [
    "from sklearn.datasets.samples_generator import make_blobs\n",
    "X, y = make_blobs(n_samples=400, centers=4,cluster_std=0.85, random_state=0)\n",
    "X = X[:, ::-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x284f5121d30>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:,0],X[:,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta=[]\n",
    "for i in range(0,4):\n",
    "    theta.append((np.mean(X[y==i],axis=0),np.cov(X[y==i].T)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "D:\\ProgramData\\Anaconda3\\lib\\site-packages\\matplotlib\\contour.py:960: UserWarning: The following kwargs were not used by contour: 'linewidth'\n",
      "  s)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_contourf(X,lambda x:np.sum([0.25*gaussian_nd(x,u,sigma) for u,sigma in theta],axis=0),lines=5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 三.EM求解GMM模型\n",
    "上面人工演示了我们想要的结果，接下来实际用EM算法进行求解，而EM求解就是一个极大化$Q$函数的过程：   \n",
    "\n",
    "$$\n",
    "Q(\\theta,\\theta^j)=\\sum_{Z}logP(X,Z\\mid\\theta)P(Z\\mid X,\\theta^j)\n",
    "$$\n",
    "\n",
    "所以根据$Q$函数，我们自然需要确认3个量：      \n",
    "\n",
    "（1）隐变量$Z$是什么？    \n",
    "\n",
    "（2）完全数据的对数似然函数$logP(X,Z\\mid\\theta)$如何求解？   \n",
    "\n",
    "（3）隐变量在第$j$步的概率分布如何求解$P(Z\\mid X,\\theta^j)$？"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 3.1 隐变量$Z$的确定\n",
    "我们可以设想观测数据$X_i,i=1,2,...,M$是这样产生的，首先按照概率$\\alpha_k(k=1,2,...,K)$选择第$k$个高斯分布分模型$N(X\\mid u_k,\\Sigma_k)$，然后依第$k$个分模型的概率分布$N(X\\mid u_k,\\Sigma_k)$生成观测数据$X_i$，由于$X_i$已知（已经被选出），那么$Z$可以表示这个做抉择的过程：   \n",
    "\n",
    "$$\n",
    "Z_{i,k}=\\left\\{\\begin{matrix}\n",
    "1 & 第i个观测来自第k个分模型\\\\ \n",
    "0 & 否则\n",
    "\\end{matrix}\\right.,i=1,2,...,M,k=1,2,...,K\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 3.2 完全数据的对数似然函数$logP(X,Z\\mid \\theta)$\n",
    "那么，对于$Z_{i,k}=1$，即第$i$个观测来源于第$k$个分模型的概率：   \n",
    "$$\n",
    "P(X_i,Z_{i,k}\\mid \\theta)=\\alpha_kN(X_i\\mid u_k,\\Sigma_k)\n",
    "$$  \n",
    "\n",
    "所以：  \n",
    "\n",
    "$$\n",
    "logP(X_i,Z_{i,k}=1\\mid \\theta)=log\\alpha_k-\\frac{d}{2}log2\\pi-\\frac{1}{2}log|\\Sigma_k|-\\frac{1}{2}(x_i-u_k)^T\\Sigma_k^{-1}(x_i-u_k)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 3.3 隐变量的概率分布$P(Z\\mid X,\\theta^j)$\n",
    "在第$j$轮如何求解$Z$的概率分布呢，它的求解可以写作如下：   \n",
    "\n",
    "$$\n",
    "P(Z_{i,k}=1\\mid X_i,\\theta^j)=\\frac{\\alpha_k^jN(X_i\\mid u_k^j,\\Sigma_k^j)}{\\sum_{l=1}^K\\alpha_l^jN(X_i\\mid u_l^j,\\Sigma_l^j)}=w_{i,k}^j\n",
    "$$  \n",
    "\n",
    "这里$\\alpha_k^j,u_k^j,\\Sigma_k^j$表述第$j$步，第$k$个分模型的参数，这一步如何理解呢？如下图是两个一维混合高斯模型，第一个模型（绿色）参数为$\\{\\alpha_1,u_1,\\Sigma_1\\}$ ,第二个模型（红色）参数为$\\{\\alpha_2,u_2,\\Sigma_2\\}$，它们的组合的概率分布为黄色线条所示，对于某一点$X_i$,它对应的$Z$的分布，可以理解为各高斯模型概率密度的占比，比如第一个模型的占比为$\\frac{a}{a+b}$ ，即$\\frac{\\alpha_1N(X_i\\mid u_1,\\Sigma_1)}{\\alpha_1N(X_i\\mid u_1,\\Sigma_1)+\\alpha_2N(X_i\\mid u_2,\\Sigma_2)}$  \n",
    "![avatar](./source/11_Z概率分布.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 极大化Q函数\n",
    "所以$Q$函数可以表示如下：   \n",
    "\n",
    "$$\n",
    "Q(\\theta,\\theta^j)=-\\frac{Md}{2}log2\\pi+\\sum_{i=1}^M\\sum_{k=1}^Kw_{i,k}^j[log\\alpha_k-\\frac{1}{2}(x_i-u_k)^T\\Sigma_k^{-1}(x_i-u_k)-\\frac{1}{2}log|\\Sigma_k|]\\\\\n",
    "s.t. \\sum_{k=1}^K\\alpha_k=1,\\alpha_k\\geq0\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "极大化的过程与之前类似，对$u_k,\\Sigma_k$求偏导，并令其为0即可得到$u_k^{j+1},\\Sigma_k^{j+1}$：   \n",
    "\n",
    "$$\n",
    "u_k^{j+1}=\\frac{\\sum_{i=1}^Mw_{i,k}^jx_i}{\\sum_{i=1}^Mw_{i,k}^j}\\\\\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\Sigma_k^{j+1}=\\frac{\\sum_{i=1}^Mw_{i,k}^j[(x_i-u_k^j)(x_i-u_k^j)^T]}{\\sum_{i=1}^Mw_{i,k}^j}\n",
    "$$\n",
    "\n",
    "由于$\\alpha_k$有个约束条件，可以通过构造拉格朗日函数来求解，将$\\alpha_k$的损失函数单独拎出来并构造其拉格朗日函数：   \n",
    "\n",
    "$$\n",
    "L(\\alpha_1,\\alpha_2,...,\\alpha_K,\\eta_1,\\eta_2,...,\\eta_K,\\beta)=-\\sum_{k=1}^K\\sum_{i=1}^Mw_{i,k}^jlog\\alpha_k-\\sum_{k=1}^K\\eta_k\\alpha_k+\\beta(1-\\sum_{k=1}^K\\alpha_k)\\\\\n",
    "s.t.\\eta_k\\geq 0,k=1,2,...,K\n",
    "$$  \n",
    "\n",
    "求解其KKT条件可得：   \n",
    "\n",
    "$$\n",
    "\\alpha_k^{j+1}=\\frac{\\sum_{i=1}^Mw_{i,k}^j}{\\sum_{l=1}^K\\sum_{i=1}^Mw_{i,l}^j}=\\frac{\\sum_{i=1}^Mw_{i,k}^j}{M}\n",
    "$$   \n",
    "\n",
    "PS：其实拉格朗日函数里面可以不要$\\eta_k(k=1,2,...,K)$项，因为$\\alpha_k(k=1,2,...,K)$从初始化以及后续更新过程中都有$\\alpha_k>0(k=1,2,...,K)$，根据互补松弛条件必然有$\\eta_k=0(k=1,2,...,K)$\n",
    "\n",
    "### 四.代码实现"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "os.chdir('../')\n",
    "from ml_models import utils\n",
    "import numpy as np\n",
    "%matplotlib inline\n",
    "\n",
    "\"\"\"\n",
    "代码封装到ml_models.em下\n",
    "\"\"\"\n",
    "\n",
    "class GMMCluster(object):\n",
    "    def __init__(self, n_components=1, tol=1e-5, n_iter=100, verbose=False):\n",
    "        \"\"\"\n",
    "        使用EM训练GMM\n",
    "        :param n_components: 高斯混合模型数量\n",
    "        :param tol: -log likehold增益<tol时，停止训练\n",
    "        :param n_iter: 最多迭代次数\n",
    "        :param verbose: 是否可视化训练过程\n",
    "        \"\"\"\n",
    "        self.n_components = n_components\n",
    "        self.tol = tol\n",
    "        self.n_iter = n_iter\n",
    "        self.verbose = verbose\n",
    "        # 高斯模型参数\n",
    "        self.params = []\n",
    "\n",
    "    def fit(self, X):\n",
    "        n_sample, _ = X.shape\n",
    "        # 初始化参数\n",
    "        u = np.mean(X, axis=0)\n",
    "        sigma = np.cov(X.T)\n",
    "        alpha = 1.0 / self.n_components\n",
    "        max_value = X.max()\n",
    "        min_value = X.min()\n",
    "        for _ in range(0, self.n_components):\n",
    "            # 每个高斯模型的权重初始化一样\n",
    "            # 每个高斯模型的均值在整体均值的基础上添加一个随机的bias\n",
    "            # 方差初始化一样，使用整体的方差\n",
    "            self.params.append([alpha, u + np.random.random() * (max_value + min_value) / 2, sigma])\n",
    "        # 计算当前的隐变量\n",
    "        W = np.asarray([utils.gaussian_nd(X, u, sigma) * alpha for alpha, u, sigma in self.params]).T\n",
    "        # 记录当前的log like hold\n",
    "        current_log_loss = np.log(W.sum(axis=1)).sum() / n_sample\n",
    "        W = W / np.sum(W, axis=1, keepdims=True)\n",
    "        # 迭代训练\n",
    "        for _ in range(0, self.n_iter):\n",
    "            if self.verbose is True:\n",
    "                utils.plot_contourf(X, lambda x: np.sum(\n",
    "                    [alpha * utils.gaussian_nd(x, u, sigma) for alpha, u, sigma in self.params], axis=0), lines=5)\n",
    "                utils.plt.pause(0.1)\n",
    "                utils.plt.clf()\n",
    "            # 更新高斯模型参数\n",
    "            for k in range(0, self.n_components):\n",
    "                self.params[k][0] = W[:, k].sum() / n_sample  # 更新alpha\n",
    "                self.params[k][1] = np.sum(W[:, [k]] * X, axis=0) / W[:, k].sum()  # 更新均值\n",
    "                self.params[k][2] = np.sum(\n",
    "                    [W[i, k] * (X[[i]] - self.params[k][1]).T.dot(X[[i]] - self.params[k][1]) for i in\n",
    "                     range(0, n_sample)], axis=0) / W[:, k].sum()  # 更新方差\n",
    "            # 更新当前的隐变量\n",
    "            W = np.asarray([utils.gaussian_nd(X, u, sigma) * alpha for alpha, u, sigma in self.params]).T\n",
    "            # 计算log like hold\n",
    "            new_log_loss = np.log(W.sum(axis=1)).sum() / n_sample\n",
    "            W = W / np.sum(W, axis=1, keepdims=True)\n",
    "            if new_log_loss - current_log_loss > self.tol:\n",
    "                current_log_loss = new_log_loss\n",
    "            else:\n",
    "                break\n",
    "        if self.verbose:\n",
    "            utils.plot_contourf(X, lambda x: np.sum(\n",
    "                [alpha * utils.gaussian_nd(x, u, sigma) for alpha, u, sigma in self.params], axis=0), lines=5)\n",
    "            utils.plt.show()\n",
    "\n",
    "    def predict_proba(self, X):\n",
    "        # 预测样本在几个高斯模型上的概率分布\n",
    "        W = np.asarray([utils.gaussian_nd(X, u, sigma) * alpha for alpha, u, sigma in self.params]).T\n",
    "        W = W / np.sum(W, axis=1, keepdims=True)\n",
    "        return W\n",
    "\n",
    "    def predict(self, X):\n",
    "        # 预测样本最有可能产生于那一个高斯模型\n",
    "        return np.argmax(self.predict_proba(X), axis=1)\n",
    "\n",
    "    def predict_sample_generate_proba(self, X):\n",
    "        # 返回样本的生成概率\n",
    "        W = np.asarray([utils.gaussian_nd(X, u, sigma) * alpha for alpha, u, sigma in self.params]).T\n",
    "        return np.sum(W, axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "#训练模型\n",
    "#verbose=True，显示训练过程：请在pycharm中使用，notebook会产生多张图片\n",
    "gmm = GMMCluster(verbose=False,n_iter=200,n_components=4,tol=1e-5)\n",
    "gmm.fit(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "D:\\ProgramData\\Anaconda3\\lib\\site-packages\\matplotlib\\contour.py:960: UserWarning: The following kwargs were not used by contour: 'linewidth'\n",
      "  s)\n"
     ]
    },
    {
     "data": {
      "image/png": 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dYL+codfOGvnR7N1YdCcY2fZtl+fsTduLWTUTbAwmwj/Cp8Rc9o89V1lKhuFTDDKGmkVv0SCsBesn9vZoqnHGIOsRZZmASe3DWeNHnPEfT7T6Mrqito5r7MLA3p6/5W4U/9VkGL4kzPqhx7bb12pP+1rtHf8e2e38uf3p+/nxoImPNn3E9IHTyxzrhVJVfNovREhXlbFrVB5XnVeMPW94SS51ZOSrq1/lrbVvkfJcCjWCarDp1CZm/TMLvU5PobUQm7QRERBB34Z96dWgl9sKRXbiE5N4/LcPOK18QIDamepFEwgyBLt4PdhXJb64Q+oNGVgjppCcf5SmyhTyc5q5CAPnd5arLCPDOJ0o82SahN7s9Z2dzjtNreBa5BXlcSTzCDtO7+DA2QMk5SbRvlZ7nr7+aRfXTQ33XEtumxqXliobeVpZG0tLDi6ha92u1AiqQZFaxMurXqZvw750rN2RUL9QTFYT+9P38+KqF2kc0pNjR/uTlGVCEQJVSqKdPuioyGOk6f9DGJ0IL3qJ6PDQUh+73cQTn5jE+Dk7sKjnJ2CdgLAAA1kFlnOCojc3NruVHt/2ICn3Dba+sNXFTOI8OQSrt5Btm02O/leSs67zON41x9bwQPwD/HH/H6w5toa96XvJL8qnVY1WjGg7gmbVNbOAr1yIuU6bDDQuhqtOsFfGxlJafhoJKQm80esNx7/3pe9jxQMrXK7rGduTMNmbBxf3onbhzcD5qFC7yajAksvE9fcQG16frWNWEO4fXnYHSiyqFCHcpuRddM8iOs3oxPA5w9k4aiMGxUB8YhLCqQmBnlB1EJmGrwgLTfb4yB6xPYgMiOSZ35+hbc22tKjegtub3k7tkNpl9/cq4koUoOUxN16J/deofK46P/bx/ZsRYFBcjl3qjaW1J9YC0LtBsdki0BDIgMYDeHbps8zfN5+tyVvZn76fY1nHmLz8e4Qt1G07JovK88tf5lTOKWYNneWTUJ+2bD8Wm6tkt9ikw6fZ7g/fYOJiRnxxlEdav01CSgLTN0933F/S2BZk7QNST0y9zV6fPbbLWLalbOPdvu8yutPoUkJ92aFlrDuxrswxXKlciI/55cBXP/Yrtf8alc9Vp7FXxsbS36f+xqgY6VS7uDJSREAE/9ft//hk8ycs2L8ARadgVs0czjjMCXMBkZZxbtuxijOkWOfzSMdRdKnbxe01JTUwTzb25CyTW81u4ab6dKzTi3+v+TcPtX/IrYlKIYQAW2cS0pZgkzaP+wEPtn+QlUdXUmApINBQ7PsupWTWzlnM2zuPlLwUVJvK5tHeJ4grlSs1Va6v5sYrtf8alc9VJ9jh8ieKSjydSJsabRyJuwBaRrXk09s+Jdecy4nsE0Cxq+CAD7d4FMY5+vkIIZncc7Lb8+4EtbMZxZk64QEeP2y/zHvItqzmsy2fER54HZkFJV0nIdqvB4dy3yExJdFrKb+ZcTNdNkgPnD3AG3+9wf91/T9GdRzFoJ8GEb8vnrjmcR7buFK5UgOBfDU3Xqn916h8rkrBfjlw1pyTA7bRvZ5rPpVf9/zKH4f/YHSn0TSp1oS/k/7mUMYhRveM5Z3FKW4yNhaRr6yie/Tt1A2t6/aZnjI9lhTudtPTs7O3u20nO6cO7WJu5vXVH1Hb9BUCV9OVQRG82Hs4I5e/w8qj3mu0CiGYvHoyw1oNo3WN1jSr3owBjQaQlJuEXqdnZPuR/Ofv/1xRgl1KyYnsE+w/W2weO5VzirT8NLLMWRRYCjBbzUgkWUFZmC0KOhmAjiB0Mgy9rEbNoLoczmhO/fD6l6UkYEl8dZHUApk0PKEJdjc4a842TBRxll3HgohPTCKuQzQ/7fqJpYeWYlSMTN88nUB9IKkFqaTkplA3tC7jB77MV2uyXLxiAkN2Y7Pm8XLPxz0+15OmJSl25yxpenp94W632jhAUlJXLMa/MOt2429r63IuyKjn4W4deHtrEzac3FDm+8g2ZzNz+0ym9ZsGwIDGA/hlzy8ADGs1jObVm5fZxqXEarOy8eRGVhxZwdoTa0lISSDHnOM4LxBEBkYS4R9BoCEQP70fOqGjeqiZk5nZFMkCbCIPKQoAOGuBxtNfwKAz0Lx6c9rXak/nOp3pWrcrHWp1wKAYLul4fDU3aoFMGp6oiJqn9YDvgFqADZghpfz4YtutTJw1Z6s4A4BUoxy2y3Un1tEztiePdHyE2368jXo16vG/wf8D4NGFj2I1bmX9xDEubT65eAmn/gmmV4NeHp/rSQMLMiqljsUnJpFXaHXbjgQC1OtA6jHptpYS7NnnCl53rtOZ9SfXe+yPnQndJ9D3+77c3fpuLDYLXyV+xeBmg4ufJSVtarYps41LwdbkrXy17St+3fMrZ01n0Qkd7Wu1574299GuZjtaRLWgQXgDaofU9qh5O6/MaoUpPHRTGM3rFnEk8wj70vexK20XK46s4Pt/vgcg2BhMj/o9GNB4AIObDSYmLOaixuDJq8UXc6MWyKThiYrQ2K3Ac1LKbUKIECBBCPGHlHJPBbRdKThrzvZkXIqMdBw/k3+GEGMIADfWu5HuMefT4ZpVM9UCqlGSjac20rVuV5b8k+bxQxzfv5mLz7pZHCRXv4gUcQpjfn1CRBxJWTFMmrcTP72ulLeMMzoC8LM1xawr/TPYl+qtolrx066fyC/K54/dWR77VTukNqM6jGLq+qkEGYJoEN6Afo2Ki3dURoDSiiMreH3N66w7sY4AfQB3NL+Doc2H0rdRX9/cR50oKRy/W2difP9mPNyhh8t1STlJrD+5nm+2LmbloZUsPriYp39/msbh7Xiyy0Pc1+Y+ooJKZ9j0RkVEUV+rhUk0vHPRgl1KmQKknPv/uUKIvUA0cNUKdmfN2SaKl/SKDHMIxMFNB9MyqiUAj3Z+lCBDkCN3TIYpg+qB1V3aU20qe9L2MCD2Ia8fclyHaCbN+weLKsnXrSPd+B46/DDYYslX1pKv/EVU0Utg6eA13YAdo2xEnrIciQ1xzrPVeaneIKIBAF9v2sKnfxS69Gvc7O2Mm73dEVg1tutYnpZPsy99Hw0jGjq8ZC6U8vhf2689kX2c/MAvyLT9jZEaVCsaTWPj7Qxv2Im4Vhcm3HwVrtGh0RiLunPsUCg1LXdhEacoUDZyMnMdzy57lhf+eIEhLYbQLnw4i7aEkZJdWOa4NK8WjUtFhdrYhRCxQAfgbzfnxgBjAGJiLm75eqlxtl3aKLa7BupDHQLxvrb3YVSKsyk6a+e55lwebv+wS54VKA7NN6tmdh4PQPXin/zagt2YLDZsFJJh/BSjbEgN8+sohGAlg1S/lzlrmE60eQbCh58uxHoHQdbzm77hAQaXxF+HUorbeGvpxlLmGjslBV3rGq0BHBPZhVDeAJxJ83aSbvuTs37/ARXCrSMJtQ5CYOBMNheVK6g8wtX5WoOsS5h1GGHWYUSEnqFXp13MSPiaXyy/YLQ1I0x3F6eyrvfaN82rReNSUWGCXQgRDMwFxkkpc0qel1LOAGZAca6YinrupcB5eb43t9ge/dqg9o7jRsXI7F2z2Ze+j1C/UGoE1SA2PJamkU0Z0mJIqfbOms4CkJsfgDs91y7Y7ELDpEvAJnKIKJqIQrHJR081wi33k+b3FoW6XdTxv45Ci81FKBl0AgQOU45B1gJqERFoKBWpGp+YxDdrz4Aex+TlCXeC7mJMMOURpu8u3UeKnEW28Qf81OZEWp4/N66y7/WF8ghXT9dm5dTkg/4j2bCtDweLFpGtn0ea3xsYbU2IsDzMtGVGt33TvFo0LhUVItiFEAaKhfosKeW8imizMnE2E4QG68hUYVC78y6KE/6YQI45B1WqHM06SoYpgx0pB8jNj8C/4F4ahLVyWYIXWgsBUIT7nOmKEC6Czqorjhw02pq6XOdnK/Y+selOAddhsqilctGAb5tp05btx2zVgb64aHVZVKQWWR5hujf/G7INswiy9iLS8gwC9x4pF9q/8gjXsq49ky0J4TaC1f7kK6vI0v/EGb8XyS24gRPZjUtttGpeLRqXiorwihHAV8BeKeUHF9+lyqWkmSDHZAMjdJ+6nDcGd6Nf6wh+2vUTx8Ydc0RsxicmMWnPTgrVLZw1fowx62OXJfi6g5kAqLK0AA0wKKW0V50MLr5eZKGTtQg06IgI8uNY9vHi8yLA4eaoSukQBnYB7ovmmpxlAnE+g0xZhIQeZ3/6/gpJ/uWrMP1p509kGWYRZO1NpGWcY5/AU5sXgjvhKiguNVhyH6BX8yhmbz7psmlt0AmHILaPS6AnWO1HoNqDXH08OYZfaPnflrx9y9s8ef2Tjr8bzatF41JREbliugP3A72FENvP/TewAtqtFEqaCQTFWnamKZ9J83byS8JBqgdWZ8PJDRRYChz3FFgs6GUdJMUC19l2PmtjsSlGFbkuz1KE4O2hbYguIZT8bcU2+jxlKQEGhSlD27J+Ym/u7nkYEBisrvZwk0XluV928HL8TkfemO5TV7nkDLFJm8s9dcIDkKJ4JaHD3+s7CTAonDFM5a21b3m9zld8yfdzPOs4YxaNoXm166iLd6F+MVpuXIdo7uwU7TK1SWD2lpOM/3WHSx6W2ZtPYivZgNONJcelw49a4l4+6/MnN9W/iWeWPkOf7/pwKueUy/PXT+zN0am3sX5ib02oa1QIFeEVsw5fVL6rhJJLent9UJsowGRRmbE6lZfjXuabxG9YemgpUYFRHMg9iU0xUajsIEDtUqqts9mB4K9DPecTb8cmpeNDdtYaDbIOQdZe5BjmoCONv1Me4I/kBD7d+ilB1r7oZWm3OlVKfth0wvFvu93+z5NzGXvTIIcHjJ3x/Zvx9G/Fyc3sKwSDThDsryezwFLKxPPw8lzC/MLK/0Ld4IumOnbpWKSU/H7/L2w/aiilOa/el+b2Xuc89u5SJtvJMGVwLOsYqfmpzNm9iTzFhJB6BEEoMgybGoWOIJd+u3MvtajSYd/3Nq7RNyzh68SvGbt0LO0+b8f3Q75nYJOrVv/RuMLRIk9LUNJMoJPFwswmskFCSnYRQ1sMpWZQTVYfW80/Z/5B+h/GUhRGiPUO/G0tXdoCiA4PJclUhyLd8VLPAldBZ88PE2l5GkEAOco6pm5ZA8DjnR/n93X93OaOccdp+SOfJvzF8sQQjBwk22Shdpg/LwxoTlyHaJYe8+OLf0AvI90KPztmq5msBVnUDK7p45PLxpv/9aZTm5i/fz5v9X6L2PBYYjv4Zl4qaUZzTpn8/LwVLDxyjNSirWxJ2sKZfNdJFjfbHzoZjtFWH6OtCX62lvjbWrsUArfjrAx4GpcQglEdR3FT/ZsYPmc4t/94O6/1fI1Xbn5FK1aiUeFogr0EJW2uellc6s4q0oHzwrh7THdHYNKgmHMCxVZcG1UgXMwD4/s348H4ZuTptjp8ykuaD+wCwV7tSGAk0vIE4ZYRWHVJ1AtpxKe3DSF27WKfxpFu+BirOENt80cUYCCffARGkrMLHfb/oMA0/PX+HH/7fq8Vn+xJzuqF1vP5PV4M7214jwj/CJ7p8ky57itpRpNICnWJ5Oh/o1BJ5PAuaFKtCQMaD6BNjTY0jGhIzeCaPPH9blJzLYAVm8hHFdlYxRksIgmL7ig5+ngQc0Aq+NtaE6h2J1DtjkLxpO/Nvu/OX3/DyA08uuhRJv85mT1pe/g27lv89d7NYRoa5UET7CWwa1uvLdhNlsmCImsAYBWnHcK4ZKpbxz2/L+FMXjYNQzuW2sx86OQg/pO4Eos4RIOwdh6145KmIIVQFFsoadnF/472ksrXGYH+3H8GCnR/U6hsA3QEqt2QlhZMW7afwOh/aBnV0qtQBziYcRCAxtUal/nciyW9IJ35++cztstYgo3B5brX+d1ZxGkyDP+lUElEkZGEWe4jWO3JgacfKXXfa7fWPz+Zn1sOGRSBxVr8DxtmzLp9FOq2UaD8TYbxUzLkDALVrlRnEM/3u9dtfzz767dhZtxMWkW1YuLKiSTnJrPgngXljprV0PCEJtjd4FyWbtqy/SSbojD4nebt28/XJD2RfYJjWccI0Aec+yADsZCNjTy3bb7W9wE+/+cF7upxnI8GPOs4XlKjCwswkGUqndgrwKBz0ubdp/K1ilRs5GKUjYi0PEm43Bv1AAAgAElEQVSq8U2S/B5DkcGEWe+lUJdIgbIRECRltSKLLQxvNbzM97ErdReAI9q2onF+B0rIGqw2K/e0vqfc7djNaAW6v0k3vgcIIopGE6IORGAotUltx5Nt/P9+2Y5NFm+CBtjaEWBrR4T1YYrEEfL0K8lXVnFCrOOBRV/zzJmJvDngQRezSln++hNunEBseCz3/3Y/vWb2YvmI5eVOS6Ch4Y6rrph1ZTBw1kCScpPY8dgOjmcd5/Otn5NekE6QMQiz1czJDDNbDvlhLLrJsTwPMCguxakB7p5zN8sOL+PksycJNgbzcvxOZm064bPN3Bm7cFeEwCpt1A4TbDXfi7/aiRDrbfjJ5khUzho+IdQah1HWByDd8B5+ttbUDWrFP5bH+S7uO+5vd7/XZ90z9x42nNzA8XHHvV53IcQnJjH+1x2Ojck0wzuYld38OngHQzq6T2/sra0nfvsPKbr3MMpGRBVNQn9uxeXu9yiL2ImezV4BBoV8Sz75ympy9HOx6k7TLKIT3w79hK51uwLQYOJij7/tR8PPB7wtO7SMIbOH0DCiIaseXEWNoBo+91Hj2qLKFrOuDDrU6sDyw8spsBTw+PzJbD+Zh1rQllrBNekUG0bC/gPk6/4k15hAhOVRDLKWi2Zm10iPZl9Plv9sHo9/izubPHXBQh3Op/JdP7G3wzQU+GozFBlBobIDoRoxyoZEWp4qkY9dj1HR0brRUf7ZB9aC1nSfusqrH/XmpM1cV8e18LWv3idl8dqC3Q6hLpGYld34qW14feGecgv2iIhDpOo/IJQ2hBW8gkEEoOK9X95y1tjH5Q6TRUWHPyHqrQSrfclTVnAk8ye6fdWNUR1GMa3vNK8VsJzjHPo37s+S+5YwcNZA+nzXhz8f+tNtIjkNDV+56mqeVgbd6nVDlSqPzv6ZFUfWQH5PAmydyM6py6p/QvBTO1Hd8hw2TKgi1XGfc/m6pCwTRtmMAPV6ftzzMS8v+OuChbpz+4DDRh5urI+OIFRyMev2YhVnsIo0dAJCAopIM07Bz2jik7jn2Jv1B00jOvLukjNea2aeyjnFkcwjdK93PoOl85igdMHu8tTcdDY7qWSiigz8bE3dmqO8kWnK5N5599K4WiNOTviLE1Pv5PDbAznmxT/cXc3QZ2dv5+X4YqF7TxffNosFekLUAdQ2fc74G8bz7fZvafVpK27pkFzKX99OyRqmPWN7suCeBew/u5+BswaSX5RfrvFraDijCXYf6F6vOwIdC/etIMQ6mCzDLHL0v2HSJWAW+ykShynU7UUKC8o5LxpwX74uwjIaicph9T1k6XCXclErTKFILQKKi030adqEMNGZUHUQZt1eThsngeEIH9zVnglD8hnZtSNnX1lH0+hsEk8nUpTTtcyiycsPLwfOF/IG97ZjT/eXB8s5d1CjLPa5L88E8fqa1zmdd5pZQ2cR6ue+mHhJPFWsmrXpBPGJSbwZ14YRXWNQztnNFSEY0TXGo62+bng13u37LptHbyYyMJI3Nt1Ps2bxHlM2lNwo79OwD7P/NZstyVsYPmc4VlvZqR40NNyhCXYfWLOvAKOtCSZlK8FqLwLU67GKNAqUzeTpl5Nt+IUMw6eEW+5GL+sA56MhS368BlmbCMsjFCrbyNb/eEH9Uckl1X8C/jW+YuT8kSTlFJep69G4EUOv1xEWkk6h8g9BSm3u6xJDXIdoRrQdwfSB0wH4fOvnGBUjal53t+0793nxwcVEh0TTtmZbt+fLur8sIgLP536ximJBrrcVm2B81f6Tc5P5bOtnjGw/0muZP1/7KcExOb0Z18ah+R9+eyBvxrWhV/OoUhF5zu6rHWt3ZPMjm3m88+PMP/wFWYGTUSmVF8+tm2Rc8zg+Hfgpiw8uZtxS90XRNTTKQrOx+8C0ZfvxV68j2/ADKjmEqP2QqhUb+UhhRkg/x6YpnE8VENch2mGHdiZYvRU4TIbhZ3QEEWotnRESiisnFRSpjmjLVXtTSc7OxRT0Bbc37sOXQ//NO+veoc/3fVj1wCpiwmKYueMNLCGnWXTrLNIL0tmavJWknCSiQ4tNEWn5aXyz/Rvua3Mf+/fW8pqzxWQxsezQMka0HeHi7eHNdux8vy9MHtTKUVzEKs4gpBGFiHPPL521MT4xyeGKCsUTQ7MmS7GoFibeONHlurJysLgbh41CVHGWo9lm9qdHUyu4FmH+YS7tzk1IcjGjCeDOTq6BSQGGAD697VO61e3GqAWjMfmPJ8r8uiMzpbc0CI92fpRDGYd4b+N7tK7Rmsc6P+bz+9TQAE2w+0RylolAcQPZhh8oUNYTqg5GoC8W5iUM5Xbvi8Hta2OTNrdJpgINej64/QveT3iCjSlfoYp0otSHsdrO/xwGHbw1pIQXx7l60c8vX8eNMTcS6hfKW7e8RV5RHk8ueZIf7/yRrnW78lD7h2gZ1ZK8ojz6NuzrEjH6zvp3MKtmXuj+AvtiQrxmF1xycAn5lnzubHGnyxjdjcnd/b5gH9+42dux6lJRZA2Ekz7srFWX9KAByCgoYt7+2dQPuZ4HZhwnOWsf4YEG8gqtjus85Xu3FwQvEqfIU5ZRoGzBqjufx6X5f4v/t1ZwLbrW7Ur/Rv356o/qmCyuE5cEVu9Lc+nn+Uklmte7/cyUzQ+RJiYQVfgmsWFNy9xkntpnKrvTdvPM78/QrmY7utXr5usr1dDQBLsvFGt2MRhsDcnXryRUHew4171RNY6dNbloht2bGuk8ozOPdX6MMZ2Ka5+6r2u5gGeXPcv0zdNBWIgoesLRrsUG43/dAbgKI5u0EWIM4cDZA45jH9/6Mb1m9uLV1a/ybt93i+9XLQQbg12CfA5nHGb65unc3/Z+mldvTvNzhZ48abbf7viW2sG1Xezrzv2pCK8Ye3vTlu0nxZRaKg+Os/Y/bdn+UvlarOIUFpFMTkYcUi2eBNwV+Han/d/SMpSIujNJTJ8DKPjb2hJk6UGgrjb3d2lK23qBJOUmsSt1F2tPrCV+XzxIHQHG6wm13om/rYWjLfsE5C4o6bs1/rzZZy5vb7kPNeg1vn5oDc2ql+2h80Tv9zhwdjDDfh3G9se2l6rMpaHhCU2w+0Cv5lH8sOkEwdY+ZBpnUCQOY5SN6N6oGrNGl9akpJSE+oUyYcUEBjUd5DF/iKJT+M+t/2H5tkhyC0uft9ikizCSUqITOoa1GsZ98+6jaWRT4poXq/E/DPmBccvGkV6QTmRAJAbFNW+5lJInlzyJUTEy5ZYpjuOe+vb1xgQWHVhCqGUoN7+7ppTAruham+P7N+Nf89Mx2GIdx0pq/+5s4oW6Yk3c39ahzGc435+an0rf7/uyK2MXgxqNIuXUANKz/T2abaSU7EnbQ/8Zb5JiXcIZv00EqNcRYRmNQdZxTECegpJ+2Wjkz0f+pMe3Pej7fV82jtroMI+B+wnhzYUneOKW/zJp3WAenv8wC+5eoOWV0fAJbfPUB+zL7CC1N0L6kaNfCMCxs+7tzEIIZgyaQaG1kJELRpZKmVsSc25nDLK223MHchex+MBiitQix0fdMqolr/d8ndfXvM6yQ8sosBSQb8kn05SJUTG6/fhnJMxg2eFlTL1lKnVC6njtT3xiEi8sfR+kJFjtf0FujOXl1jbVUUUmEX61ERT76JcMKHJnuzfr9qGT4ehLVFVyR53wAOITk+j29nJi3r2ZXWf283KX71hw///YMulOr6lzhRC0qtGKT257j8bqTMItD1Go202K31OYjAt5vl9xURRvRUT2nQyhVtG/OZWdTrOPevLzloOO854mhLmbDEzrO41FBxbx+dbPyxyjhgZogt0n7B+rQjDBah/ylT+xku7V+6NpZFM+6PcBSw8tZcraYg05PjHJbb50dwLLRgHJfk8g/HcxZd0UXlr5EnP2zHGcH9xsMM91e45f9/zKiHkjGDJ7CAMaD3Dr6rctZRvjlo2jX6N+PH7d42WOd+rS7WSKRQTYrndMOBfjxugL9kRjb97uOTf5+P7Nisv/OVGkO4bR1sjFLu+OAINCr+ZRTJq3k335szHr9lOtaCy/rIss14QV1yGad4ZeRy1xF3UKP8Pf1o5U5Qte+msUs7ceQudBow4PNDBp3k6yc+oSVTSBfNsRxiwazW/bim36nv6WkrJM/LyqFR2ievD8H89zOOOwz33VuHbRTDE+4Ow9EWodSq6ylBzDHNoEPev1vsc6P8aGUxt4ZfUrZGZHsGRzo1IJobYez6CgqLS/slWkYLQ1ZUyb93m6Tw1+P/Q7yw8vJ9AQ6MjjPaLtCG5tfCvHso5htVnpUrdLqXZOZp9k8E+DiQqM4ochP6ATujI9Rg7kxWMz5hJqdd00vZRFlo9kHgGgYURDj9eUTNAmsWHVJdEx6kayU1wrURkUQZBRT7bJ4hhjcUEUEzn+c/BXOxGk3oxJLX+91K3HMzBZbOiJJKroVXL089ib9S0PLoijhnwNHa4TdYBBQUoc/QuwdSbcOoIsw3c8//v7DOn4oVdPo+TsQvQFo8B/G48sfIRVD6zSTDIaXqkQjV0I8bUQIlUIsasi2rvScK6Mo5c1CVb7kKss5f4bvadaFULwv0H/4+b6N/PhtrGcVde6nDdZVGZtOuF2sw+gUPcPPydsY+NBK/0b9adT7U4sO7TMUYHnSOYRwv3D6VSnk1uhnpybTN/v+5JblMvCexYSFRTlNtrS2cySa84l1zgHf7WtS255uLRFlvefLV4NNIls4vW6uA7RbJ/crzii9MUOSMw8eF1XRyUquxln2r/asX1yPxftPznL5CgUHmq9w9FmUpbJY+WpksQnJrkUNBEIwqx3Ut0yHrNuL2nGN10Ckuyur9klImlDrf/CX+3AUctnHMo45LaqlDNWSzVqM5o/j/3Jt9u/9fqONDQqyhTzLTCggtq64ojrEO0iOJoHjsRPb2BFctklXv31/iy8ZyFGtQlpxqnkKstdzntKK2CUjQhWbyGV33hn6U5qh9Sme0x3ss3ZpOansuroKhbuX4j00MLBswe56ZubSMpNYvG9i2lXqx3gPeMgwLQN07CSRU35sMs1l7rI8q7UXVQLqEbNIN+LeRzLOgZAg4gGPpWYqxMeQKGyHSH98bedD7gS4DWtgh37pOiOIPVmIi3PUKjsINPwteO4vUpWyUlRoCOyaCw6oefRRY9yR/s6bsskOmPN7Un3et0Zt/R5urw936eJSOPapEIEu5TyLyCjItq6UnEWHFsm3cUrN7/E3L1zWXJwSZn3hvqF0j5gGv629mQY/0OG4XNHbVRvBKo3ApJ9+cURqq1rtCbcP5y/T/1N7wa9Gdt1LHpdaWvaogOLuP7L68kuzGbF/Su4MeZGxzlvm3uHMg7x7vp3ubv13Xw0dJiLBuwpM6KnfYPykng6kXY123k1MZR81rwd2wGoH1bfpz6N798Mq3Ico60h4pwV0l0KZE/7Cd5SKQAEq30IsQ4iV7+AQt0/wPlVjjuNPMRQk1FtXmTV0VX8tu83x9+YJ+EeHR7EnQ0nk2POYm/BN2VORBrXLtrm6QUQn5jEovWdMNhiGPLjw8zavLfMeyYO6EB9+Toh1jvI1S8ixW8cRcL7ZqRR1idQvRGD32lGzR/FrtRd/HnMc+a/rMIsHl34KIN+GkRseCxbRm8pZaLxZE6pHebPY4sew6gYeb/f+z5pwGWZdXwlryiPxJREutX1HITj7lk/bNkGQL2wel6vsyf2iusQTWhQLiGG8543nlZM7iZAX/YYwi0PobfVJMMwA3+DcKxySq767JPlf+NeoGVUSyatnIRqK540vBX7nrlGnjMFLsYiTgOXfmNb4+rjsgl2IcQYIcRWIcTWtLS0sm+4QrELjpRslciisRTJdJ5Y/ITDu8ETcR2imTq0A22CnqGGeTJCl0+K/3Nk+r2HRXi+N0Jpw4f9P0Ii+WDjB9zX5j6Gt3YtjlFgKeDjTR/TZHoTvkz8kue7Pc+mUZtKFbAGz0KjdbNNrDy6knf7vlumO6Sdssw6vrLm2BpUqdKrQa/yPUueRk+ISxBWWYm9pDBxZ4fGjgnLk3bsbgL0ZY/BIPwJt47AojvGsO7ppXz/S06Wep2ef/f8NwfOHnB4PXmaBKA4G2aY5T4EikuuIfs+gaa5a8Bl9IqRUs4AZkBxoY3L9dyKxllw+MlmhFnvJdvwA8///gFDOnq3uZ8P6ulNrvk5pqydwnsbPiLH/0/81U6EqrfQI6YvSZm6Uh4r98qvUKXqML3YpI2E5AR+2vUTM3fMJMOUQa/YXrzf73061PYcrOOuWtC/ulqZtO4NBjQewKOdHvX5XXgz65SHRQcWEWQIcjEZ+dKmVaSis9Uo8zo4n9hLb9S7ZE10lx7B036Ct1QKdmxSkvTvKdR5/1uOmf4AHvB4rZ0hLYbQuFpjpm+e7pi03QWAdZ+6CgA9kQRbbyVXv4Aw690YziWe85Q6QePaQ3N3LCclBUeYdRhm3R6OyOmsPT6Em+rf5FM7IX4hdIl8ilhLO9LkQvL0y0hV3uXXlPdpWq0dA9t0pUlkEwoNqczfF4AqVTJMGRzPOs7O1J1sOLmBtII09Do9dzS7g3Fdx3kVjM44C430gnSu/9/1RAZGMjNuZrnc6Dy56JXHe8Zqs/Lbvt8Y0HiA14LO7p5lFSmE6hv51Cco/u0iYiI4azrrOOapLJ47weic18ZbP42KkT4N+/DX8b88XueMTugY3XE0E1ZM4FDGIY+1ZZ3/9kKtQ8nVLyJHH0+k5XwqCnepEzSuPSpEsAshfgJ6AtWFEKeAyVLKryqi7SuNkoJDoFC96AXSA5/njp/vYN3IdT7XBp22bD8WSwjh3EuYdThm3V5Muq2kZO3jh50/kGMunepVEQq1gmKhsD3Vi1rTIPhmRjS5jhtjyv8hmywmhsweQnJuMmseWlPukmzl0XbdEZ+YxKQl33DGeoZdB9sSn5jkUSCVfJbEglWcplej0gnKnp293a3tvE54AGFhMQ5vGjvlSY/gKWMnFG/E2sfevHpzZu+ezQ1v/0FKdpHXCQPg7tZ3M2HFBOL3xfP8Dc+7vcb5b09PNYLUnuQrK4mwPICO8+aoSxlvoHF1UFFeMfdIKWtLKQ1SyrpVVaiDext1sCGMD3vPxqgY6ft9Xw6ePejhbleSS0wQ/rbWRFgfIrJgKlkTskgbn8buJ3azdfTW4nqr447z822HCMn6hMD8sQSpt5CabShzw9Kdl4jZambYr8NYf2I93w35zq0ffFl4sgX7IiTtexXHzPEoshqm3HZex1HyWRGhaSBs/KvtDaWuu69rjMd86S2qt2Bf+j4sqnevJG/ePu7+BgRwX9cYx9gPnC6ugJSUXeDTxnJMWAwtqrdg5dGVHvtU8rkh1tuRwkyestrluksZb6BxdaAVs74APEVu7krdRa+ZvTDoDCy/fzmta7T22k73qavcan72WqYVcU/J5FIAfgYLIXWmk5C6ii9u/8KRgfJy0n3qKo5m7yHF/2nCLCMIt94NnB9HWdGxX277ktELR3PgqQNug5o83T9712zunns3mx/ZzHXR17m9Dij1zuxukdFO13jrX403+pKhJlC38HuXfnn7bUfOH8nig4s58/wZj+/Nub/hgQb2qI8DCrXNHwIXVrRb4+pBK2Z9CfG0dG9dozV/Pvgnfb/vy03f3MTcu+aWSnnrzIWYMsq7YVnSS0Qli+PiTcyp+ytNqENxf7OMPyJkICHW212Ou8t0WHJT8K/jfxEVGFXKHl1SUH84vL3Lb9UjtgcAH6+by659mS61Ve3P8dPr3HrWOF/z9tA2HgV0gaWAs+om/NXS1Zzc/U72Pu/JU8kypDJ7yyGGX+fezl7yb+/BX+7mu71TUEUqMWH1LyhtskbVQ/Njr2Ba1WjFxlEbqRNSh37f9+P9De97zO54IaYMT8ts+/GSJgRn7d4s9hf7z+uOEGWeWGlCHSAk9AgmZSOh1iEoTvZhd3ViwdWN0iZtLD+8nN4Nerts9vriV18ruBZNIzowZ+9sMk1FpfplsqhlFtIuy6Xz7bVvYxN5hKgDS50r+fs591kni9/DSwv+9sltMT4xiZ2HirNKGoITNaGu4UAT7JeA+uH12ThqI4ObDeb5P57nth9vIynHs+24rEAgZ7wFr7wcv5NnZ293EWwAEpVs/WxO+70A6KhpfpcmoX0qYqgXhE3aMAV9hV5WI9Qa5zjuqU6sHbuvdvRL73Em/wx1/Fy9gMqaEOyTXvqZbpjFMcy6PRc8Bk99nLtnLm+tfYte9YYRobR1OeduNeba52IFwGyRZcYC2CeEszmRKLaanDZvdQRi+UJFRQxrXJlogv0SEeoXyty75vLJrZ+w5tgaWn7akul/T7/oyvPegldmbTpRyhukULeHFL9xZBm+J1C9gTrm/xCub3ZJ876Uxf8S/sehrB081ek16oVXK7Va8bQqsed0yVNWIqQfizbXcRFI3sxUzppxkNobnQwlW/+Tx1w7ZVGyjzZp46NNHzF8znC61u3Kovu/9Wk15txnq0gHqUNHaJmeLfYJQSDwt7WkSLffJRDLGxUVMaxx5aLZ2C8hQgievP5J+jfuzxOLn+CZpc/w6dZPeb3n6/yr5b98SqHrDk/BK84iqkgcJsvwEyZlE4otippFLxGgdvP5GZeKpJwkXljxAr0b9OaD259CDCrtN+9u78G+eamSS76yhiC1B0UWPxefbW9+9c6asQ5/wiz3kGn8gjzlD0LUfuUaQ0nNOyE5gf9b/n/8dfwv7mh2Bz8M/YFAQyBxHQLLfM/OfS7SHcIgYxAoZXq2OAt+o2xAvliNSg4KoWX6sXtb2WimnKqBJtgvA42rNWbZiGUs2L+ASSsnMXzOcBpXa8zNtUfw147mWCzFttWLiRxMzjIhsVCg20ye/vdzWQwDCbOMINQah4I/R6feVuFjc6asSUpKyWOLH8OiWphx+wyPwVDugobswi9XvxApzIRYBzvGbcfbZvSzJYKKQtTbMKkbyTB8hiLDCLR1ISLQgJS4tbErQmCT0jGugW2jiN8Xz+dbP2fZ4WVEBkTyv0H/I5IB9P9gs88Ttb3PeZZMCnW7CLUO9ikWwMWn3VYceWoVZ1Bk2dp+RUUMa1y5aIL9MiGE4I7md3B709uZt3ceH2z6gK93vwaKgr9oT6DaBX9bW6Ql2mfNKT4xibeWbuR43hZMxgQKdJuwiXwUW3XCLQ8QYh3oCFy51L7NvniyfLP9GxYdWMSH/T+kUbVGHtuy3+P8DrpPXcWJrBRy9L8RqN6AUcYCruPyFkVaMqhIoKN60SRS/V4lzfgmjYJuR1j+RWZOZKmMjwK4+/poHrjJnw0nN/DLkS95ePnvZBVmUTu4Nm/1fosnr3uS1XvzynwH7sYJ8Mzil0C10iBwIK/dWra7onMglkIYADaRA7Ls37oiIoY1rmw0P/ZKJHrSJ+QpqylQNmDVFWfq08lQjLZYHry+G3VD61I9sDqBhkAEgkJrIZmFmSTlJLH++G52nN6JVaSeuy+YAPU6gtSe+NvaIzi/wXo5fJvL8q8/mnmUdp+3o1OdTqx8YCU6Ub7tnfjEJB6KH0W2WEEd8ycYZL1S4/K2YnDnzw9go5As/Q/k6heCUNHbamKQ9RweKjaRj1WkYxXJSGEGoEZQDW5tfCvDWg6jf+P+jvw9FxKXAMUFU9p81oYBjQcw9665pcbtaUwvx+9k1qYTmMVhUvzHEmV+iUjlxjJ/a3fvQvN/vzrQ/NivAmLDWpKU1YBw68NYRTKFup0U6Q6A4SRz9sxxyWniTLAxGJslCqPajGB5O/5qK4yyMQIFRQhUZPH/SukIqLnUH6y35f3cbSd4eNFg8mw2cpPHsGB7Srn7U63aYbJ1y6ij3IWxsF6Zgruktuwpz4sOf6pZHyHUGodJ2UKhsh2rOI1FnKS4PlIgelkdf1sbavg3Y/7oB2kR1cJlYrILX285ajyRV5THsF+HYdAZ+Kj/Ry7nyhrTm3Ft6Fy/Gq/+fpQUC1QPCmLKwLKFc3ny41wqLmRvScN3NI29EilLczJbzZw1ncVkMSGR+Cl+RAREEGQIouGkJW79OQRcclu6Ozxpq+EBBpLUWaQr3xFZ9BzBai8CDAp3dopm9b40nz/sxxc9zvIjy/nnsX8IMgb5/HzAZXKLnbj4gsfo7t16WgmUfL47jT2/KJ87fr6D1cdWs+DuBdzW1LVtX1cA8/bO485f7iRhTAIda3cs56guP9qK4cLxVWPX3B0rkbIClPz0ftQJqUOjao1oXK0x9cLqEWwMRghRZqDS5caTf72J/aTrfiDQejPBanG+dXut1/K4231626esfXitW6EO3rXipCwT42Zvp8O/lxNk9FxXtCzcvduyqip52gg9mX2SnjN7svrYar6545tSQh182+SMT0xi3NwFIAVPfJt8VbgsevLKeX3h7krqUdVDM8VUMuXJLOjMxWZWrGjcLe+fvqUe9y8ahUIk1ZxSy4L7cnSvLdhNXIdopJSlPGaEEF4LgHhL12sns8CCQSdQdALVdr4HOgGKTmBRPa9eDYpwebdlmV8Aj2awOXvmMHL+GPKLCqlufokvfq9LqK10ZsuyNjntmm+qSMAgGnA6W1wV+dg9TViZBRavGT41fEfT2K9SLiaz4qXsk3MU7V+pH2LVJVPd8qxL2oCSqGRjFWlkmPKYvfVQuXLC23G3YnCHxSYJ8dO7vLcP7mrPtH+1O585MtBQ+sNwkvnOAT6esJtLnH+P41nHGTJ7CMN+HYbFXJ1ahR8RYOviccXiLcoYiifRXGsyZt1uAtWuwNVRJs/bqvJK7/vVgqaxVzCXc1PoQrX9y8GyQ8v4bOtnhFji8Le19XidSh7pxg+wiRyMtgaMiQ/ljeU38Oatd5VrbM4rhrI092yThe2TSwcl2dvoPnUVmQWuvuwWm3S4oZbX/JJdmM2769/lg00fIBDEKI9A3u2OgtrgPkCorE3O5CwT2Ya5gI5gta/jvkeLSiUAACAASURBVCvdH318/2Yei5Vc6X2/WtAEewXiiy/3tUCmKZORC0bSMqolodmPkpLtWQhmGr7EaKtPhHUkJl0CFt0JjpuW8cicI4yd3Ye64SE+T472ia6sDc3yRHW6O+5N+IQHGBACnp29nalL/6F54w0sPPopGaYM7m1zL1NvmcpNb//j83O9Td4hocc5VrSUEPVW9DLKcfxK90eP6xDNawt2uw0Eu9L7frVQIaYYIcQAIcR+IcQhIcTEimjzaqSiijtf7fzf8v/jTN4ZZsbNZMKANm7NCYGG4j89g6yDXtYtPm7rRKD1ZvzVDph1R7CKMxeUx8RupgoPMJQ652tUp7fjns6HBxgwW21kFBSQoyxmq3kEM/e8Sf3gNiSMSWDW0FkkHNGVKgJS1nPdkZafRqrhHfRUI9xyv+N4Ze6zlIfXBrfyambSuDguWrALIRTgv8CtQEvgHiGEb7XhqhhaqDYsPbSUb7d/y4TuE+hcp7PHvYApQ9sSYFDwszUnVz+fXGUREhU9kQTauqCTweTo5yKxXNDkGNchmu2T+/HR8PaOZ4cHGPA36Hh29navGQ17NY/yetyT7Rsk6bbVJPs9TobxM/S22tQ0T0Wmv8jTM7NoMHExz/2yw6Obqq9C7WzBWQbMGkB2USpv3fw19cKjrph9Fl+52D0iLTuldyrCFHM9cEhKeQRACPEzcAdw4TlRr1Ku9VDtvKI8Hlv0GC2qt+DVHq86jrszJxRaCylSm/DxCiMyx0aBsp4sMZNAtTt+shkBto5k63/F/ifqaXIsK9rUudpQXqEVyzlvGG9mstX70tw+y37cne17aJciXlo9DrNxHwZbLDXMr+Fv64RAkFlgcdjsVQ9xI9JNP9yxL30fcT/HcSzrGPOGz2Ngk4E0jTg/TvsEeLUI9/L009kTyTntg/NvCZUbeHWlUBGCPRo46fTvU0D5C2hWAa40F8TLzeTVkzmefZx1D6/DT+/n8bolB5cwZ88cVhxZweR+k4kUDzFuXgjZbCPT8A06grCKVMKswxDnDBfuJkdvexrgWt6u5GYoeM5o6MvKyy6UTBYTr6x+hRfWfoiihBJZ9AxB6i0uKR18IbqMyV9KyYyEGTy3/DkCDYH8cf8f3FT/pmtmX6fkON25y76+cDeFFluVfxe+UBGC3Z3JsJRaIoQYA4wBiImJqYDHXnlcCaHalcWO0zv4+O+PGdNxDN1junu8rkgt4vU1rzOl9xRGtB3Bf7f8l3f69ODft/Xik9V1Scm+FbNuBwYZg0HWAzxPjmXtaXjzXLHjToh7WnmFBxroPnWV47e9+wbB57ueYk/aHsZ0/H/2zjMwqmprw8+ZmklPSEhCKKEJoSaAFClSlCICoQhyRQWx3kuRqyCiXsAGihf1gqjY+UA6hN6bgoCUEHqVEEgCJMCkzmTKOd+PcYZMpqYgAfP+UU722eXM3mvvvda71nqRThFjeX9NKjqz53aLwtPmn5SRxJiNY9iduptH6jzCD/1+oHqgxS5xr4fg9ZZF5omJBCXbvO93lIdgvwLUKPLv6kB68UKSJM0F5oIlpEA5tFshUZEpiHcKoiTyyrpXCNWEMv2R6W7LfvjrhzSr2oxudbpxS3eLLRe2EKQO4nTWafo81It3Hn6HxKQOXi328rBpOLsJOLt5KeUCeXqTTXicy9nJ2O0zCFT7s/GpjfSo1wMAP2WQV5RLK0J8lUzu09jp+M7dOMe7v7zLgqMLCNWE8l3f7xgeN9wuTk15fIO7FbdlycELTFy1nXzzNczym5zKzeWFlXrmnQykTriG89fzOJiSS75egUwKQC4LQSGFo5CikOHrdTt/JxuXFeUh2A8A9QVBqA2kAU8C/yiHeitRTrjTC3f+0fnsvbKX7/t+T4gmxGU5URIZGDuQmOAYAOYemsvzLZ5nZo+ZHL12lCeXPUnHWh1JiO/sVf882TS8Ea7ODKXObl75hSYbPS9PvpkbytmopLrU4z2bULe+mxAfTe2J67zKzeSrUjiM9WTmSabtnsbPx35GLVczof0EJnaYSLBPsNOxlsWu81epcrIKsth7eS8H0g+QdDWJ49ePk6K9BArJQQolnleiuqjAYBKRMILSMWewXKqCSqyDSnwAH7ExQfLGaBQ+lRTKP1FmwS5JkkkQhFHAJkAOfC9JUmXQhwqCO71w8wx5vLH1DVpHt+bZuGfdlpUJMppGWNL4mUQTw5oNIzrQ0odmEc3oWrsrqdmpHtt0ZUQDe7WGp+Bc4NpQWly4W9vIk2/nhup/+JhbEG6YxI1CH6fvexPiAOxPk/uv7Gfa7mmsOrMKX6Uvr7Z5lfHtxxPpH+ny/bLade6UKqfQVMjOlJ1sPL+RrRe3cvz6ccAyBxqGNaRt9bbcymyHQopCIVVFLoUgk4KQoUH2ZwaptDxL8DsJAyK5mIVbmIVMjLI0jEIqBtkFdIqDZAsS2XJfmoV3xJDWDIWhNTI0Jf4W9xPKxUFJkqT1wPryqKsS5Ys7rYP9aPdHXM27ysohK93GWP/ywJfkG/M5lXmK1x96ndjwWKIDoxElEZkgY+/lvey7so8Pu33otj1nRjSrcHcWm6W4YC4Od2yb4gJTJ0vmhvJzfMzNqWp4GwGVy9Pg+B4NGL802cbCcYWoIB92XNzBe7+8x46UHYT4hDD54cmMaj2KMN8wt+9C2e065UnRNZgNbDi3gcUnFrP27FpyDbn4KHzoWLMjQ5sMpUPNDrSq1gpfpUWN0v6c8+iV1YI1tvYFBATUyFCjkMJAqo8gYhtn51g/frn0C5vOb2L12dVkyDch0/jga+pEXc0gpvR67G+nGoVKz9P7HneSW38l5wqf7P2EoU2G0rZ6W5fldqbs5L97/8t/u/+XbH02j/7fo4yIG8F7Xd9DJshIzU7lw90fMq7tOALVgW7bdLZRWYV68dC4Re0drkLguhLMxdsxkUWW6iOUUjThhkkIqFDKBfILTdSeuM5BoFr/68rDEkBSniE7YAld5+0nyj+KTx79hJdavYS/ynVcHWcoi12nPCi6Z7LO8PWhr5mXPI8buhuE+YYxpPEQEhom0LV2VzTK23UVDRPu7rbhyk7h7Hfu26AvfRv0ZdZjs9iTuoefkn9i4fGFJBs38/XJnkSGT3Y7P+9HVAr2+xx3kls/dedUzKKZD7p+4LbcurPrGNpkKP0a9qNfw348F/8c/1r/L+K/jmf54OVE+EUwqcMk2tVo57HN0m5UJVVZFK1PQuKG6jMkCgk3vIkcPxsv3iq0nam4igtcqwopNfsSBb4/cFP8lQh9BP/r+T9eaPkCPgrnap07iZJ+l6L2Gr/As6hD1nD4+g6UMiUJDRMYHjecR+s8ilJ+2+t34bGFyGVy+jboazdGT7eNkqqYZIKMjrU60rFWR2Y8OoOvDn7FzH0zafddOwY1GsQnj35CreBapftQ9xgqozve5/AUIbA0SExKI/7DH/n28PeECX1JTlG5Lf9E4ye4mneVy9kWd4faIbVZ/9R6+jzQhzkH5uCn8vNKqINnd39XcOXpCDj1YCxaX758C3r5EUKMI4kJeoCL03vjq1I4qFk8ecj2aR7JoIeTuRkwCr38EFM7T+XCmAuMbjP6rgh1KJkHqFU9dSHnEBmqiZww/pvka0k82eA1Lo+7zJInlvBY/cdQypUkJqXRbtpGfP/zIC+v/IiZu79n1PpRrD6z2qH98T0a2NQvMzadsYXuLYtnaogmhDc7vsnFsReZ2nkq68+tJ/aLWD7b9xmi5GiMvd9QmUHpb4DyZMVYF3cqH6KTHyRa/y3+ylC3i+5GwQ3e3PYm+cZ8pnaeSr3QegBo9VoGLRnEggELiPCPKFH75ZF9x11dYDkx5hmzSfd5EaVYnRhpBtMHNHfLenGVwSo9N51hK4axI2UHvev3Zk7vOdQMurf8OVpOW8hp3WwK5L8hl0IJND6Bv7k7NYKD7dQj1u+aa8rglvJbwg2T0CjldGt5HJPiPMOaDaNDzQ5IksSqI+l/STal1OxU/rnun6w7t45utbsxf8B8t0bpiorKnKeVsKE8ufUzNp0h23SBAp9fCTQORk6QS2OsNWFGFd8qzO0zlze2vMHAJQN5Lu45Iv0j2Z+2H7VCTYR/hNebT3k6gbkzLFsF1b/W/RvRlEtDn7FM6dXc1k6QRulUdx7kJPDY/iv7SVicQE5hDt/1/Y4RcSNKFXPeFe40nVWUROYcmENS4XiQSQQZnyLQ1B8ZlltGUbVVgbGA6RuT0RklZARiEP6gUDgLxgfYd6oG/+gsY+WplTSPaE6AOsBtNqXiYyjLOGsG1WTN0DV8l/QdYzaModXcVqx6chUtq7Us49epmKgU7JUoESwxwBchSBoCTf1tz9O0OjuvTGeL7qNHP2JA7ACWnFhCZkEmBcYCfkr4qcSUzKIbVYo2hQNpv7H+nB896vZALvPeld+Tvv7BunCDVTwb9ww/JrxoV8aVXC7+fP259QxaMoiogCi2PL2FJlWbeN0/b3Cn6ayZ+Zk8vfJpNl3YRLDsQfx0r6CQqtqVsaqt5h+dz+f7P+ekTo2vvB1+5s74m7uTr9iFylifG9n+tIluw7LsZVzJuUJseKzDb5Cl/ByTkMZVk0CLOWE0jKhGlH8UufmhbDyiBEMMMvxKNU5BEHi+xfM8WO1B+i3qR6cfO7F88HJ61utZ5u9U0VAp2CtRIgQHXifFsIdA0xPICbA9F7jtEJSSfZGXVi5l86Xa9G7UmPioeFtauzbV29Cmun0ooRmbtpeYkpmWk8aYjWNYeWol0p9KkdiwWH4b+ZtTRx5n8GRYnrZ7GmbJzOSHJzuU0TpxXy/+fP259SQsSqBpRFM2PLWBqn5Vnb5TFtxJOmvy1WT6LOzD9fzrfNn7SyJkjzNp5XEHtclr3eszbuM49qft5/u+3zP421WcNc7A19wRH3Nz8hRbyJdvoUFAP9rXbM+b294kIy+D2PBYh99AQIaAAgmJc1nXyDFdIT03HZ1JZ/GS8RFQSrXRmFtQaGrH5NVCiU/xzSObs+/5fTy24DH6LuzL+FbfsDO5xn0VBqRSsFeiRAiOWI9wWUWgqZ/tWXEnoUzVu2jMbVh27CJB/rdYe3YtvR/ojSk/nhmbznAp+yLRgeG82bMlCfHRJWK6JCal8faGJZwyvAOCmUEPjGFSl+GcuH6CYSuH8eWBL3mz45sex5GYlEaBweTw3GpYzsjN4NvD3zK8+XBqh9R2KOdpU9h3ZR8DlwykaURTtj2zzevNpqQoDUvIG5XGtj+2kbA4gWCfYH4b+RstoloAllNv8Xd7Nq1CyOW+fNrzUwBe7nCd/2xvhUlIRy01wGy+QYFyM13iLGoPP5WfzYBZPJtSFeNo2/8LBjj/n95IkkTNN+dhkF2iUHYWvewoOYpEcpTLyBKr4Z/XkwB6kKbF61N8pH8k25/dzoNfd2ba/heoangPH5rcN4HDKlkxFRgVLeb05ezL7E5PpHfdYdQMjrSxFYoK9ULhDHIpnBDTs/jlj+bJJk8SFxnHV/tWMGblPC5rs8iVbyQj22BLoOEt0yUxKY0xK3/khGECMimESP3nHDvZk5SMcJ5q9hTNI5qz89JOj+Owqi+KB40K1ihtRruZe2diFI1M7OA8b4w7ttHl7Mv0W9SP6IBoNj618Y4JdSg5S6hovlaJ26qbonNry4Ut9P65NzHBMex/fj8tolrY5uK4P4XwR4MaMqTLcepWu4lZNNOldhcA9l7ey7QDT9G2dhS5mlnkytdRN6Ajrzw4kt8z59NkThMaVGnAI3UeASzC01lCFLhtrxAEgZrBNdCILQk2DSXSMI0a+vlUMYxFLgWjVX7PFZ/n0CoWkW/MtzFrPK2dYJ9gQgomI5ciyFR9gFG4CtwfyXEqBXsFhTcL8K/Gp/s+RZIkZvd5xy5pddGQs3KpCmYhi3zZHqoFa2ge2ZwBsQM4edmfLFYhoCLA9DgyNLYF5C0lc8qGDVyRfYBSqk5k4QyUUrTdIgz3CyenMMfjOFxFCvRTW+K23NLd4qtDXzGk8RDqhtZ1WocrOl7vZlUZsmwIOqOONUPXEO7nPGlHeaGkdFZPETF/T/udhMUJNAhrwM5nd1ItoJrDXLyYfZJn1nZnUfImZv8+m6HLhwKWOTt6firKrI/Iu/ocUzt9SmjkFua/VJ/20X3IuTKG7NSJHDjS124eT+nbGKXM0WiRbzDZyhUfpwx//M2PEmn4mEj9Z/iITclWzidd/Qrnc3Z7vXYys1VUNUwGRLJU0yyxabj3A4dVCvYKioqWZi+nMIdvD3/L4MaDHZw8ii46BWEEG5+hULmbhvV/Jacwh3C/cKTcHoCAXnYCBbdd5dO1Oq84y3qTnpOF7yFDQ9XCKXb6fesizMjN8EqP7Ul98dXBr8gz5DGh/QS39STER9ttcAnx0bz3y3vsvbKXb/p8Q2x4rMe+lBUl5Xu7G3taThp9F/Ylwi+CzcM2U8W3CuA4F41COkpzPYSbr/F1n6+5ln+NoYte580Vx8jM9kNOGGlaHXO3iVT1acjyIyd5c8UxrmYLyAlxELQJ8dH4+zhqhY1myS5xSPFxhvhaTvRqqR5VDW8TUTgNGT5cV08mjS9tQhpcr51qwRqUUhRVDP/GILuAVrHA9vxeRqWOvQKhqO6zpLFN7jR+PPIjuYZcXm37qsPfilMQ6wV0onuLhuRwkLEbx/JI7UdQa/IplE4RKtmzS6wLyBMl871d72GUpVK1cKrdxgAgEwR+/v00p7NOMyB2gMexuNKPywSBxQfP8/n+z+lRtwdxkXEe6yqKwxmH+fDXD3m62dMMaTKkRO+WBSWhs7oae2SQksHLBpOtzyPK8CFt3z9o06E7zjkJmRTAFe1NAOb3n0+z2Z0JNtVAjcVHQcREGl+TlpGCMcuEzmh/hixu4HVljHaW3MSK4owgH7EptcXZZIjfkatYjUG4SFXDW8iwhGhwNm6r5y3GNvibupOjWEGo0IXxPfo5lL2XUCnYKwicOcs4w904SYiSyOzfZ9OuejtaR7d2WsaZcLmkbc/u1N1M2TGD6+ZIgs1PO1DlrDRJZwY860Z3WZtOmua/NAnujSmrNTrR/huZJYnxa+dhlpvpVrubx/E4c6O31jN29edck1/jjfZveKynKCRJ4qW1L1HVryqf9/y8RO/+lXAVQiCm9mYWnfmNauY3uGWwOIulaXW8uviILZOOhISAgEKKJFe2mrAgPQD1q9THKBq4oZxJNcMcCoXzaJU/oZAiqVLwIZkuFAPpWh1avZbj14+jDNhNVsENJKEQkCGTfJFLIUT718Esmm001uKG34Eto9lxOtPOmDtjkz9ncutzQ/k519RvUbXwA+T4I/z5ftF5VvRQImpHoFfswz9yAf3iXinfD/8Xo1KwVxB4kyHmboUg3frHVs7dPOeU9ucOtYJrUSu4FnPWR2Ew5CK4mG5pWh3jFh/h1cVHbBEa4XaskGzFKkTJSEFWf4a2jGbh/ssOuUNvsAo1EW6zN1mREB/NwUs3mb/PPkSwhJkbwjL8hYZ0julcorEKgsCXvb/klu6W25j0dxvOHLyGtIPXfvmcMFlXlLqOtrJ62Ql0sv0opGr4m7shcFv14Ss0xDd8GYWmJ9h0YRMB8toYTEqMZGEWslCJD6CUqlElKBcfIZIr2gJbmkMrqgVr+HTvp7z7y7uWB04iU2QaIWj6GDrW6kgt34fZfrguBqMlOmSaVsfyQ2lOVU/jFuuQS/5cV31ApmoqEYYPAJVTGmjRQ8ms/ZmM2TiG7Re3062O50NCRUWlYK8g8KRikQvCXctA/9XBrwjzDWNQo0Glej9dq3Mp1K0omph43OIjaJQydEYRCZE8xVY0YhvMxkh2nM5ELCbU9bKjFMpPEmp4CYXMvh1X1D5ncdjz5b9gkl1Fox9ZKs/QVtU8enpXCBQVZJIk0W1eNwLVgWhujrSV0ctOkKX6iCDjUxTIf8EkXMVPbIVabEK1YA2f9fgfc46PYObemcw/Np9udbuy4exu8hVbMcr+QJBUyOV6HqgtY0iDcYxflozRfPt3U8oFxvdoQGyNaMTCeizYo8doDECGGgkRkQLMQhZG2RXgHMkZx9iYvxFBrsKPrgQZn0RBmFPOfkJ8NK8uPoJGfJAww+tkqadzU/kVVYxjPK6zF1u+yLTd05i+Zzrd6nS7a9mlyopKwV5B4CkxgyhJd2VCXc27yuozq/l3u3+7TVBdHKnZqSw9sZSRLUZ6nXTCCgkoMFp4zkYhBVHQ4mu2BAmzLjBrfRJGbiq/Ri5Vob6/vV7UnVdm8QUuYSZHsQSlGEO9gM5e9/Vex7pz69iRsoPZvWbz8/ZI23c1CpfwNz1GgLkHPmIzdLKD5Ml/4eCbT9uczRrW+B+Ljy/mpu4ma29+Q7OoTpy8/juhBW9RM7g6Qx+SszZ1GpdyTjlmQf7z3w3CGrD9SBqiUWdL/y0AMnxQSKGozQ+AriuKQoiSLpCrWE+efCv58u0Emf5BoKm/U2Ed/ecc8RM7YDA+QY5yKRpzK+oHuj+FqxVqRrUexVvb3+KLX39l9ub8ezI5diUrpoLAGW2tKO6WlX5e8jzMkpmR8SM9Fy6CH4/8yPgt49HqtR7H5g4G2QUA1KJFPWM9NVnr0yr+D6PsElHiGCb2bGb3rjtmUfHvWSDfjVF2mWDTECb0vPNslooASZJ4Z8c71Autx4stX7RnN0kR6GWHENGjlKLwEZsSqA5i8fHFtvcbhjVkcufJ7Bu5j13Dd1EzNJABTdtwefoz7JnYlVGdHuZyzmXm/3bTIRKmUbzNePGGEGASQUM9qhhHE134NT5iC7TKH7mu+g/hQQaH8kXHEmx6CpVYl1uqrxjVrbrHtkbEjUAmyJi+a26FYqaVBGUS7IIgPCEIwglBEERBEO6Ne2gFhZXO5cxZ427p1iVJ4scjP/JQjYdoEOZ9+5Ik8X9H/4/OMZ2JCY5xoKqF+Cqd8padwSxkAxZ+vPU7WOtTBOwiR7mCCFkfZvUf6XCKckftK7rwJcxoFT+jFGvxQquhbk9jC44u4OuDX3vV94qODec3cOTqEd7q+BZKudL2XUN8lajEBqikeuTJtwAQqKjD4OYPcTXP4sSz6vQq5ifPZ1fKLkJ8QmhTvQ3LBi9jTu85tvrf2PIGnWp2Iivbz2n71t/H20OLWZLQKOUopAjCDW9RxTAWvewkxwz/5qd9R+3KFl1PAgpCDa9gEm6y5sI3HtuJCoiiU61OXDP+4rbfFRllPbEfBwYAzr9AJUqEhPhojkzuzmdD4kodh7o8cTD9IKeyTjEibkSJ3juUcYjzN8/zVNOnHDwWPx0SR9J/ujPjieZ2jk3OEKxREqqxeG2GBxXavoMkSaQalvOH6RMerfMolyctd/p93HllFt1s8uXbMMnSeK3NO3zQv7nL/uhNev6797+2QF4m0YTBbOCm7qZX36U8UR5eyZ/t+4zogGieavqU7VlCfDRJ/+nOrCEdiPZpjVF2Af/AM0wf0Ix/te/Fzks7MZgNiJLIx799zPQ90/nm8DesP7ceURJRyBRk67PR6rVo9Vre6PCGR+9Yb2901rUQ4qtEQMDf/ChVDVMolDJ4eeMTLDl4weGdQpNFpaeWGqIxP8iS03NZfPC8x7Yer/84RlkqJsHRFnMvcNzLpGOXJOkUUK4hSCtRvmF2y4IFxxagkqtKbDRddnIZCpkClbENb651HXnQOsa3E4+xYF+qQ1LqKX0b07BGTWK/+IywqA18sFHJK0v/QK9ZgVb8nYSGCfw84Ge7bD1F4Sk7UEJ8NN2bhPDArGdoE9iGD3s953Zck7ZNIj4ynvY123M9/zof7f6I1JxUqvpW5dG6j5LQMMGWw/VOojwiOl64eYEtf2zhvS7vOf1+CfHR9Gz6OvOSqzL30FzqR/dg7dmtRPpHYjAb6B/bn+zCbJacWEK+MZ8N5zZw8dZFtl3cxpg2Y+gc05mvHv8KQRAY30Pp8XcAXKbDA8sJ9FZ+oV1cGQCN2Jwww3gy1e8zdsPrDG610va34qq4AFMC19Vv8c6m7xnSyn1u3a61LWGbJeVpMNz2HnZ1e65oRtZKHXslnMIsmllywpIRp6SxTladWWVZ2Duue6WjfD+hKZ+6uKU0DGtIr5hn2XxpPgcNg7mqnki2+RhVzS8xrP7ndvk0iyMhPpqBLaOR/3nwkAsCA1vab5oz984kLTeNGY/OcHtAyTPkcSLzBEbRyIWbF3h57csEqAMYGT+SZhHNWH9uPZIk3XGhDuXjlfxT8k/IBBnD44a7LOOj8OHFli8ytMlQPt//OStOr+CzHp/hr/JHlER61+9NvdB6tIxqyfMtnmdf2j42X9jMwfSDbL+43VaPN7+D1Ys3ZXpvPhsSZ/MqBdAoZSDcNqgXh6/YlgBTH66KiRxKP2R7Xlxl4iM2RS6Gc6Vwu8dbTpOqTVDL1dSKvO6231Axw394PLELgrAVcJZq5C1JklZ525AgCC8CLwLUrHlvZY65V1GWU8Tu1N1k5GXwZOMnS1TfH7f+4HTWaV5u+TKfnfA+8qCzW4q1vSvaQUQKzTHKriCgRGN+EBk+zNx8noEtXM+lxKQ0lh9Ks3HezZLE8kNptKoVSkJ8NGk5aUzbPY0BsQPoWKujy3oA/FX+rBm6ho/3fMwTS5/AV+nLlM5TAItKZsXPK/g97XeHkMR3AmVNUC5JEouOL6JLTBeqB3o2Jr720GsYzUa7k71MkBHuF07fBn359vC3LBq0iCs5VxgRNwKtXkt6brpto0xMSmPxgct2v8PiA5dpVSuUHk1C2XdlH6eyTpGtz8ZX6Uu90HrsmNDedqBwlYi8KIKNw9ApdjJ111RWD7Wk33MWElgjPki+fAdXtHlubzlKuZII3xiOXTtFFRfzx4o7GTq5tPAo2CVJeqQ8GpIkaS4wFyyp8cqjzkq4Rlmv68tPLcdH4UPvB3qXqL4tFyzGth71erAkOL3UibSLticgoJYesFDfSoMWoQAAIABJREFUisCTIPO04F7b/Bpm0cyMR2d47A+ASq7i7U5vM6jRILIKsmzPT2ae5FreNVpWa/mXXMnLmqD8dNZpzt08x7i247xuc93R607H9UidRzhx/QQTt05Eq9cy67FZ5Bbm2iU8mbrmhB2HHaBATGPk6lnoN/xCgbHAoT21XM2wZsN4r8t7Xm1YfspA+j/wHMvO/o/L2ZepEVTDqSrOR2xEnmI9RiEVnbG2W+Gbkx+EAXsduzOBXdaN9k6gksd+n6IspwhJklh1ZhXd63bHX+Vfovp2XrJEBGxQpQHjewR4zDRfXBB2aRjOjtOZXvHeZYJA7YnrXApQdwtu6x9bWXxiMZMfnkydkDou28gz5JF4OpEedXvYIjU2DGtY5BvoGJ44nIkdJrI2+dodzWZkhSfbgSdsurAJALmhhcesV2C/yRYK5zmde55nEo8y6EIXZvebQI96PXhxzYuMaT0GgAB1gN37RcMjS0jkKhK5pZiHIMkY2eRp+sf2Jy4yjlBNKHmGPI5fP87i44v5MflHEk8nEhU4mdwc17+R1XmvUc06LD37OavPrOZfrf/lVHevFC0B7Iyyy6jMtd0KX6PBD7MsxeF58XfKutHeCZRJsAuC0B+YBYQD6wRBOCJJUo9y6VklyoSynCKSryWTmp1qF0LA2/p2p+6mY82OCILgMT+ps1tAcTd/d7Be7V0JUFcLLiJI4OW1L1MvtJ7LeOtWjFg1gkvaSxxIO0C3Ot3o26Cvre8fbzzJleybKALa42Ps+Jddycua93VHyg6i/GL4dOMtt5uQwWzAYDbYjeumahYac1vUxodYfnIVSTdWMbr1aH4Z4ZkYJyFxS/k1uYq1aMxtCTW8wjd9n7Er46PwoXNMZzrHdGZs27H0XdiXlNx3qCL7FETHyJ1KmcCMJyy5aFcevoKKKryxZhkzV9bGLEm2EBVW4a6QLJuzWbgBuBe+/ip/dOZCh+fF3ynrRnsnUFZWzEpgpceClfjLUZZTxJozaxAQ6F2/d4nqy8jN4ErOFdpVb2d75o7h4018HG/hTIC6WnCRNRLZf+EC25/Zjo/Cx2WdqdmpHM24gJDblwUpWSw+OJf59bbTLqo3c7eZ/1QTqRFze7oN4HYnruSlZU5JksRvl39D0Ld0a4CdsekM53N2kqmeTqT+E1TUpVA4B8gINlnir/sXdGB2r2AmbJ3AT8k/8WO/H51mmwr+M/F3nnwDuYq1BBgTCDGNxK8IxdG5CqshG4dtpPlXzalRZxW5af+0SyAerFEypW9jEuKjSUxKY9LK48iEmhhlaQ6bfouaQaRpdQhY4syIWNQ/XRq6jpffvEYQ21LsDerOBLa7jfZusWUqVTH3Kcpyivj56Bp8hQfsQre6ioiYX2iyRcxLupoEYEuj5gnlLfCK1+dswT3eKoe39szlpZYv2bL+uMLhP+SYMkdhMobii5FCXQTbT59h29mZyMxx5KnW42vuRIC5JzqjGbkgOAQng4rFe07PTSerIItQQ4zTv1sFoc5oRqc8CpKASrIYqFVSLVTiA+TJd+Bn7oRcUJB5I4Y9z+1h8o7JHEg/4FSwP948ip/2HeOW8gd8zPGEmJ5DQEBvFG3MkeI3t3GLj3Dw0k3eT2jK8ObDmXt4LtpJC12yoKyHBJkyENOfmZCs0BnN7Pvj1p//shfUO05nuhS+EUECob7+RPtoPApmV8b/v0I15wyVgv0+hXXiTF1zwqbjVCs8U/EWHjjD6RuHCDQNtKNuTRvQlGkDmtrVB6DVGW2T9VzBCQCbA48nBP15kisvOBOgRRdcbmEucV/HERMc45XB9OONJzEbIxDAwsYRW2A0RGAS0slRrMEkZBJgvp3h3uoZWZGu5MVxKusUAFF+9clzkmxKLgi2/huEc6jEuoDyT3GoQmNuQa5iLSbhKgGmnryxwkIv1Jl0bL+4ncGNBzvUueN0JvnynUiCjhDjSIQ/WdYi2G4IxQ8MErBgXyqtaoXSoWYHZh+Yzdzf9rBkr8ypkPV0SLBuuBKWcgKWuVJ0Iyv6b4AbuhtUDwpnz0td3dbtCneTLVPJY7/PoS/C/bUKYXf82nc3LwNBxEe8nWSi6GT0VTmeBax/P3vjLOG+4V6FrU1MSiPfSTLp4pDLBIfwA0q54zNvBOioDaNI0aYwr/88BwNfUVzNu8q0X6dxvOBztIqfkbi9OJVSNBrxQQplZwgxPm/3npV/XxG8hl0hRZsCwJiHOzhNqVf0xmGUXUEpWYyNEhah7yu2IcQ4EqOQynX1FK5K83h57UtsurDJZcapdK0OvfwYCjEalRTj8DdXQlnCIhytvgGfbT3nkitu3dRF4RYyAh3qsnLRrbp1uRRie+5K+KZmp1IjqIbTvnmDu8mWqRTs9zFK48iSrjsEkgK12ND++Z+T0d1kvZR9iZjgGK/7VpwC5wwBaoUt/IBVWM4Y1NzhmScB+tORn5iXPI93Or1Dh5od3Lb58tqXuZR9ieqaDhTKTpGhHke+/LZx0E+jJVh6FF/xNme9aByb4unyKhIycjMAGN423ukmZA3zIFKIKOTYjI3RwRpbuGSVFEO48Q2qGP6NQooCXTu+7fOtS3ZRtWANIlpbXUUR7Kt0q6pK1+o4mH4QkGE22htPi87l8T0a4KOUYZClohTtufkapZyhbWqgUcoxCpcBUIrVHDayokjT5nH+5nnqh9Z32TdPKGmi8fJEpSrmPkZpTgyi6jRq0wPIsA/Ra52M7oyoGXkZ1A1xnvy5JH0oimyd0aWhsHiaNFfUveSrybyy7hW6xHThnU7vuG3v4q2LXM27yvf9vueXaB1vrojjhmkPt5Q/UCDbS3XG8UHfzkDnCuVC7i1u6W/hp/RDJVe5/K5vrjhGrjEfAJkUgEpZwJhHGjBjyyGysv1t5VRSLVTmWkQHa3gw+kGXbY7v0YCnEgMwcs3hb3l6E72bRTmElLAiIgjmHZ2HxhyPDEdDt3UeJcRHk5Z3gVHbtajFBjZ7R3SR36ZVrVBGrZsHJjm1AmOZ2LOpyzAGwYGZXDLqaR7hOnaQJ9xNtkylYL+PUVJmjN6kR895AgX7uOZFJ6O7yfrP7TdoE+2d56W3MdqL99WZoQscjW9WPWnHBj70X9yfEE0ICwcutHOccYbaIbXpVa8XC48t5MWWLwJNmbFJRZq2DTq/L3iqjdEmDO8FQV4cepPeYxgGgPc3/kqaAdQ+16gS8QOfJc+kWvWmXNTfQmFsjo/Y3KIrV54nrnZ9t3z4hPhoBp17lHmnPsQgpNqMsWAJ37vjdCZPta3pINx9lDICIudxLfUajX0mkesYnddufmilXwFImvAGNYMcPZIT4qN5/8BZYhRt2f1cL9tzZ/O5bWwmyUehXY12DvV4i7LSUsuCSsF+H6OkJ4aj145ikow837o7u485ZwK4m6zPbsq3OTSVpm/OUJR144ploFbInKqcPtp4nP8d/Yi03DR2Dd9FhH+E27YkSUIQBDrV6sT7v76PVq9lbNux9G7WEaVcyfTdx7mcvQtwNBBWdFg3xGP5l9ApjA65P4siIT6a9g90o+onkCVuQ0wZRzX/GOJayqiiOcfaE7+TZ8gkwNydfOEAG5KrIoqOPgVwe56EB7VEkDTcUH1OROEHdqfvdK2O9xOa0qpWqK18VJCK0OhFrLu4iEkdJvFg6AC3c9loNjL38Fy6xHRxKtTBYl84lHGIad2m2Y21aD+t89k3UIZR9pzXN1BXuFsB/SoF+32M4pM2SKNEEGDc4iPM2HTG4fRgDaD0z/bd+ah3Lbf1OpusJtHkkJrO275ZvU7XHc1wYN2MX5psK+tMgDvbHCQkjhd8Ql7KDuYlzKNt9bZe9QugS+0uRAVEMX7LeLYt3MagRoMwmA38fOxnPu3xqdf1VBTYbYgKFWap0CPt7pfTBSAJSFIgSrEuN3OCWbpbTs9m1VGbBW7IV6OQquJnGErx0Fw6o5mpa06gN4q23+Z6tpow2TgyVdO4pn6TKoYxqCQLNdJ66k6Ij6ZfXDW2X9zOxG0TWXfxIOPajuO9ru/ZDKiuTr8/HPmB1OxUvuz9pcvv8OORHxEQeLLJk3bPnc/naLrX7e7x21ZUVAr2+xzWSesNpzbpahKhmlCXJx5PkAtyzKL3DkfFF1RiUhoL9jt6nhpFiSmrT5BdAmpktuJn8hRbeafTOzzd/GmvHEWKRndsGNaQNUPXsPLUSo5eO4qfyo/RrUffkwmOi26IMvyRBD0FRr1b2t3MLRdQSBEIElxTv02QaQiS8SFWHxZRSA8SIBPJl2/DR2xsS3JdFEU3Zyt8xYcIN7zJDdVsMnxGoxTrEEBLYus34ZPfDnPuxjm2XdzGhVsXiPKPYvGgxagM7en40U67g0lxZOZn8tb2t+hQswO96vVyLIBFBfXVwa/oWa+n1wb+exmVgv1vAm84tcevH6dp1aZexdd3JigD1AHkGnK96o+zGDHLD6XhgqSAVme05bEsjhBfpd3pMEe+mmzlQrrWGMLUzlM9bmqns05z5OoRagTWQEKifY32tm/QP7Y//WP7ezWmioqihmq5FAqASbhButZ5HHvrOypVHQzCHwQbh6OXH6FQdhKV+AB+5k4YZOeRMDkV6u7gKz5EjLoV5/ITEVVJaFnBd8eXwnHwVwajMDegiqE3tQy9OHoumuWHbv9uRX0erL+hKIn8dHYUOYU5fNn7S5dzd+6huVzLv0bqpW5u4wvdL6gU7H8TeGLISJLEqaxTDG0y1O7vzgTw2uQMp4tMFRrMtXxH5kNxOBO0rlgRRZFf6Mh71yjlTO7TGLBsXmdyV3JLNZc2kT3YNHw+giC43dR6Nq3CE0ufoGVUS/7I0nL+qox8/WfE+D7C1F59LFmtrh4hNiy2RMm8KwoSk9KQFfGIVUpRAJiENGKCHL1EragWrCE7tzEFqt9QSnVQmmpSKDuBTnaQbMVC1GIjQkzDS9yf6GANeyb2BiybpVk0c0t/i83Hs3h3zUWb30VGttnjnNAZzYxdP4kr5tV83vNzl45xN3U3eXv7FHzF5uTmNEDAcXOfsnMKj9Z5lPY125d4TBURlYL9bwJPDJkbuhto9Vo73m5JgnTpjGau3wrkWu5Rt4a5xKQ0XluS7MAf9iaOc3Ev1RBfJZP7NLa1dc28lpfXzeax+o+xYvAKm77f3ab2fdL3xEXGkVDrA8Yf+gXRnIJMdpqLug28tkLJxeyaGJVJxEXGOa2jIsP6+xX91tbohpIihfE9XCcoH9+jAa+taMctvkEn/40g0yCU5uoEmHthJgcZvgglFB/ODPdymZww3zC+2H7UzpkOPM+JbMVytOb5jIwfyejWo12PZfN4cg3ZRBmeRygSUkBnNDNl9QmO5nzHlj+22BysKlo2pNKg0kHpbwJneSWLLrQ/bv0BQN3Q2yyAkgbpUoo10YlpjF38O3FTNzt4uL6deIxxi4+4dAopKXxVCtuC++S3T3h53cv0rt+b5YOX252u3TmKNItoRlpOGh9s/A2jMRAfsRm+5g4IkprrLGPZPjmvtHqlXPrrCeWRx7QonP1+cgJRitWIqXbFrbBKiI/mvwO6EyA0Jk++GQnRFgpATmCJhbonJ7KSeGNKmLml+A6t8geqyG6n4HOGVadX8f2R7wkyDrAZa4si1bCC7w79zJqha/BV+vLFr7/y2oqtXNJeqTDZkEqDyhP7X4y7dRrwxKm9nG3xyKsReNuFuqSuz2rxARDMFMrOotU1YfzSZKauOYG2wEiwr9KpQa0oBBxPacFu4smka3WIksj4zeOZuW8mgxsP5v/6/x8qucqunDvaZ4ea0bSIasGX52fhJ3sYX7EtSqkaIaZnuaZ6m5TsUwSoSxcrpCS4EwGjXP1+arEZp27tptBU6Fa9lBAfzVzl2wxdPhSfgIMU5rZ2256EiFYxDz9zVxtXXaOU2wl0V/H3XW31xeeEiSxuqGailx8lWOzD14/PQiFTOF1XTWrpGL5qOC2iWqC68TwZ2Y6qPAEV2jwfsvXZbDi3gUk7PsYgCCiUEajFpvibu9z1bEilQaVg/wtxN6O9Wdtw1U5GnsXVPDrw9gKUuYhW6Ao+YhOQ5OhkB/ERm2AUJZsw9yTUNUo5A1tG25JsWD0H/dQKBMH5+xFBEgOXDCTxdCKjW4/m0x6fOnVA8rSpTe08lcQDk7mmP4henoyvuR0gwyi7TM3A0ruUlwR3ImCUK/VbDZ9OnDJsZOsfW20ZslzhiUZP8O6ud9Hq5hGgb0mh8fb3VcoFkCysJQCzkEW+Yit5yvWEGv5Fff8eTOjZsNTx9+3nRC5GzWau8hOSZKKu4nWebPwMM7dc4LWlx+02gDStjvErdqMLfgu5IGfpE0s5mqJ2SIQNEGDuQV6hxIAlAxAlEX/dK8gkf3TyQxTKTuNn7oCA8q5mQyoNKgX7X4jyXrzldfpPTErjo837QRJI+F8yXWMj7XKFegsZ/viIceTLdxJsehoB916eVlgz4LiiZSplAkq5YBdbRqbMIF39CQfOnOOzHp8xtu1Yt22429T8VH581HM0ryeuIVtM5qbyS9RiIyLEl3mjZ2MvR1823ImAUa5uKlN7PslLW2cw7+g8j4JdLpPzWc/P6DG/B+1jt5Ge2s/B69c6B2sF1WJKp818f2ose6/MoFXNY1zMHkf76Za/l+SgYLWfdG8SQq0a+/hoz0dcunWBbrW78dXjX3H8ksZubEVrFckjVfYOxrxUfhmxnTohdagTApNWHKXAKKKTHUYhhaOULLfTBgH9GdfxYYLUQUxZKidNq0MtNqFAvgeRQuS4j2dTEVHWDEozgD6AAbgAjJAkSVseHbsfUZ6Lt7xO/9Z6srmFTO5PerbBIxuhaBwOK03R2o8AU08y1R9QIN+Nn/lhr/owtE0Nu1N18c3PKEoEa5T4qRWkaQtQBuzhijQLP5MPm4Zt4pE6pUvLK0kS2YXZBPsEM7BlLeSy/szY1Ih0bQKRQUre6Nm4TDepkmy8dyK9mrubyp7MZ5hzYA7puelUC6jmtp7udbszIm4EPx6ZxaZhj/No3d4OY/t0SJytveFtf2HW/lm8s2MqG89vRG1uhr+8Kxrzg8gJ8thvER16eTLrLi9lxOZlaPVaWkS1YPWTq3n8gccRBIFn5253av8xo+W6ejIG4RJVCyfZAr4lJqVhFCWyFUvIUSTia36IAFMv/IR6lm/SyNL3/B6W9XBTWosg+SLHv8KFXvYGZT2xbwHelCTJJAjCR8CbwBtl79b9ifJcvOV1+rfWIyp1CJKlH57OVNa440WDK1njtGvENijFWmgV89CY2zgN3FQcO07fThjsapPT6oy82iOCdZe/ZNnJZXSs2ZEFAxaUKazqB79+wLeHv2X/8/uJ8I8oV/fvkm68dypglKsxjWkzhlm/z2Lm3pl80v0Tj/X8r9f/OJB+gMHLBjOl7TK+2mp0OTaFTMG4duNYtLMOZ42J5Mk3cEP1GQBKsQZKMQaFVBUZAQiSEkkwIZKLScjEKLuEUUgFk8jl4370j+3PCy1esKVbtMLZPDEIl8hUvYtZ0FLV8Db1Ajva/jZj0xkKzbkYlZcJNg5DwkyuYhM+gsCMTT6MW3yEqCAfXutRn6ja33MtLYMq+e/cs6yYsqbG21zkn/uAQWXrzv2N8ly85XX6t/HYMSCg8lD6NopuIkW9W2dsOkNhzitcU0/klnIuocbRdhQzT312tvlJmMmTb2LkxnnI5AY+7PohE9pP8BjQyx1WnFrBOzveYVizYVT1c8ylWVaUdOP9qwNG1Qmpw1NNn2LOgTmMbTPWYYN0dttYM3QN7b9vz/idgwgzvY+KGLdju56tIIhBBJoGYhDOo5cnUSg7jUF2jgJhLwhFjJmSHLkUhlKqjsbchuq+LZjSfRAfrDvPM/tzgfV29Nbi8yRPvoObyi+QoSGi8EOCFY1s6yoxKY00rQ4Z/oQYn0eGHyYhA0nQk8kGdNkG1DQkPVvP2ytPMuChx9g24lmvHPUqKspTx/4csLgc67vvUJ6Lt7xO/9Z6JMFspxN3xlApDmep6BLio4mbakJnHEyOcgkyKYRg0zCEP8W7szqL9rlLw3CbKkhCRCfbj1Y5H6PsEmpzE2JV/+bNjiNKNMbiOJh+kGErhtG2elu+6fPNHVnApdl4/+qAUe92eZclJ5Ywfst4Fg1aZHvu6rYxbUBTtj+zncazH+KqegLhhjfQiC1t7xUfm3VuCQiopfqoTRZDtEWVJxIZJFA9VMGBizmAxnYA0Cjl9G8UzaQVp22GWbAY0Mcvs8QNsh6S8ow3uKn8mgLFr6jNjQgzTKBWcA27nKNjVyzEKGgQUKKULN9XKdXA1wwF8r3kK3YgMwWikx3CZGrNzuQYhF73rlAHLwS7IAhbgUgnf3pLkqRVf5Z5CzABC9zU8yLwIkDNmqWLRXI/oLwWb3md/q31FBW7RdkI7oxezjaRxKQ0tDojwQxDFLTkKBdjkl0m1PAKckLcpo5LTEqzGG0pIF/+C7mK1RhlqSjEaoQVTsRXbI/WULYFl6JN4fGfH8dfWQXT9deIfXvbHTkd3wmdeXkjJjiGSR0nMXnnZP7R9B/0bdAXcH/b2DOxK3Hq2RzVT+K6agqBpoEEm/6BgMphbK7maHE+u7PbwYxNZ+yEuhVGs8SMTWfYOb4j6y8e5IdjH2OSdNSUP8fMx//DwJb2weteXz+TdNkCNIq26GQHCDEOx1d8CLAKdyV62WGuqd5CQE1A4WP3HAPGGTwKdkmS3FqmBEF4Fngc6CZJrk3ekiTNBeYCtGrVqnw8VP7GKK/Tv7X882tVGEwmu8QEVhQ/wYHrTcSa0UZARqhxNAopGq1iHjqfw0TIe/JCu2GsPeDH1Wyzrc+PN4/gZOZJXl//HenCXvQ+h5GEQpRibaoYXsPP3Ml2myiLYMwqyKLn/J7kGfRU1b1LptE+72XR71FW3M0kCyXBxA4TWXl6JSNXjyTppSSqB1b3eNt4u2cn3ljxKel8SY5yGQXyvURKL/J69+fsyns7R50ddsY5oSYCSBg5k7uVRnNe4vzN83Sr3Y1ZvWYRGx5rX06SyCzI5ErhRsKNb6GS6qCTteCm8itEUyH+Zksic6UUyS35IRRSGBGGDxGQV6jNt7QoKyumJxZj6cOSJBWUT5cq4S3K6/SfEB/NmtQ6bLxwlj3/vu2MU/QkFeyrRK2Qka0zut1EigoFAYEg00B8zW3JViwiS76et/ckIhNkBIeEc7VQwaBVesTVWlteUbmsCn7mR/A3dUElNbDTz5dFMOYZ8uj9c29StCnUl00n12jf9/J2QrmbSRZKApVcxcKBC3nwmwcZuGQgO5/d6fG2cXtsgVzIaU+2z1yuSJOZkbQRNOPp06CPLZxDaedo8T6YhOvkybeSp9iIWbhJDVWcHUumOARBoKpfVUJVDTGZbqCUaqIRW1LFOJos5UwESYWf2B4JIzLJlzDjeEvC8gq4+ZYGgptDtueXBeE8oAZu/PlonyRJL3t6r1WrVtLBgwdL3W4lyh+vb36dOQfmUPCWZX92dUr3lFu0/fTtLiMw7pjQmp0pO1mYtItNp09iFAsRUCKXQvGT1SRI3oACXaRTY6tcEPjv4OalEhJ6k57eP/dmV8ouVgxZwdgf5E51/QJwcbp7Xvf9isTTiQxYPICEhgk8Ve9T3k48ZffbWxV1zm50BrOBH5J+YNruaVzKvkS1gGoMaTyEhIYJtKveDqW8ZBEgAVYcvsyry1eRKxxCJ9tPofwUSAK+Ujz/bvcq7/YY5tE2IkkSTy95k3UnTxBQOMKW7tGgOMQt+RKqFE5AQRVb+eKxhyoiBEE4JElSK4/lyiLYS4tKwV7xMGPPDCZsnUDOxBwC1AEuBbQlOp9rF3tvNgRXdbsLH1BaoWswGxiweADrzq1jXsI8nm7+dKnHdr9j1v5ZjNk4hiGNhzCo9nQ+3fLHn8ZPe6O3qw3eJJpYc2YNPyb/yMbzGzGYDfgqfWkd3Zq4iDgahDXgSpYvqw/ncSNXICLAlxEdavJgHQ2Z+ZlczrnM+ZvnOXrtKIcyDqHVW1xiVGJdfM0PEaV8hA/7dvNK8FqzYRnNRh765jFSM5X45I8gOiiUCT0b8umhURRkDiMr26fC3qacwVvBXul5WgkAqgdaMrunZqfSuGrjUtMpi6ogrKEBimaTB1zmOs3WGV0K92Dfkp/6DGYDQ5YNYd25dXzZ+0uebv40cO/ov/9qjG4zGr1Jz4StE8g15LLp34vpMfN3h9/LldpKIVPY4tfnFOaw9Y+t7EzZyb4r+/j60NfoTEXq8YF0IyTtAHbcfuyr9CU2LJbBjQbToWYHutbuagtz4Qlnss6QZ8gjPiredutTypXsfXEDg5cOJsx3C02rNuXgrR3kmFPY83ovfJW+pfpWFR2Vgr0SgIXXDHD+5nkaV23sFavDlWeldcEXp8yNX5qMO0q7tY7xy5LtwgeAheoW/+5mr6/KhaZCBi8bzOozq5nVaxYvt7qtIbxX9N93A+PbjyfIJ4hX1r1C++/bcyN7NAqiHMp52uAD1YEMiB3AgNgBAIiSSOvpS0nLuYJZyEUSdEhYKLZhvkH8NPwRqgdWJ9I/0pYGryRYcHQB0/dMJ9gnmNiwWOIi43gu/jl8FD4oZAqWD17OvOR5ZORlkJabxpant9y3Qh0qBXsl/oSVVXD8+nH6Nezn8VTrybPSVWgAVxCwcNgT4qOZsvqE01P7rQKjV+yVAmMBAxYPYNOFTXzx2Bf888F/OpS5W0mG7wW82PJFYoJjeHLZk+T4jCXY8DJ+5i52to+SMkdkgowb2f6oaejgzKDLhXH/l0e6NqlUm6zOqGPh8YXM7z+f5pHNWXR8Eb+n/c7Hez7mtXav4afys4QhiHsWsCT3KItz272AynjslQAsJ6x6ofU4lGFJaJ0QH820AU2JDtYg4BhP2x3XGUruASsByw+lkZiU5ja3aXG1TlEkJqXRZtoqQt97kE0XtvAe9Jz3AAAO3UlEQVSv5jOcCvVKeEb3ut1JeimJB0KbcEM1k0zVVIyCJQJoadVWrjYDa0ajssQ/zzfmcyn7EgADYwfSu35vcgpzWHJiCQC7UnZx5KqFQnm/C3WoFOyVKIJ21dux5/IerAb1hPho9kzsysXpvdkzsavdKcqTDr40XGCr0Pb0rrO2E5PSeH3FdpL0YymUnSWscALbDjW55xIkVCQkXVQQnPc+IYYX0MtOkK5+BaP/T0zsXa1Utx1nyV6ceSO727ydQaPU8K8H/8V3Sd9xMP0gSrmSjrU60ji8MTtSdqA36Um6mkTtYNepAO83VAr2StjQtXZXrudfJ/lassey7rISgfNF7A3StTqP7zpre+Lq1aTIx2ESrlPVMAU/sYPH0315Ziuq6CjpeK2qtvRsA4HmflTTf0WQ1IUM8zL+ub0do9eP5kyW98IXnN8CXSnn3N340nPTmXtoLkUZfb3q9eLhWg/zzaFv2H9lPyq5ihHxI7iUfYnr+dd5te2rBPl4jix5v6BSx14JG3rV64WAwKrTqzzm+PSkg7ee6JzlN3WHasEa27vOdO3O1ACTNvzAWenfyPAjsvAjVFId299cne7vZsKTvxqlGW9xVZuCKgQXjqV24D+Ia7yLrw99zewDs+lYsyNPNX2K/rH9vQqmVty24Yp6WnzzTs1OZc2ZNaw4vYKdKTsRJZGHajxkS2Dtp/Lj6WZPs+DYAibvnMzQJkMpNBei1WvxV/l77Nf9hkoeeyXs0OWnLqTlpHFm1BmPDiDexBt3xWsf2DLaLo679bk3cUSsfxclkQ9//ZB3dryDSqxPeOHbdg4n4Jyb/nfjsZdmvLUnrnPrxHUt7xrfJ33PT8k/cebGGQQEWlVrxSN1HqF9jfa0qtaKCP8Ij31zNj98lBL/fMSX4OAr/Hb5N3ak7ODsjbMANKjSgCcaPcGwZsNoEOao59eb9OxK2cUPR37AR+HDhPYTaBTeyGM/7hVU8tgrUSo82/xZRqwawc6UnXSp3cVt2eKnL+t135kQdiacW9UKLVUcEYBbulsMXzWc1WdW42fqTKhxtM2zsCicGfnuRLaiiozSjNcT3XXvORNr97RBr21K88AMYuuc5lL+Xmb8NoNp4jQAqvpVpUGVBsQExxDlH0WYbxj+Kn/UCjUCAkbRSIGxgLDo0ySnXcYkZGESrmKWpzN2pyWkb6A6kI41O/Jyy5fpVb8XDcMauh2rj8KHHvV68EidRxAEoVTUyfsBlSf2+wxlTZenM+qo9VktWlZryYanNnjdVpBGSb7BZMc/9yYEQWmw/8p+nlz+JFdyrvDf7v9l0fbGpGfrHcoFa5Qcmdzd4Xnlid0Cd+N150EMuPzbo42DOZh+kEMZhzhx/QRnb57lkvYSV/OuYhRds51kUiByqQoKKQKNUJ2nW3bghbaPEBse+7cVzs5QeWL/G6I8dMcapYbX2r3GxG0T+fXSr3Ss1dFpueJtOeOdl3dgLZNoYtqv05i6ayrVA6vz64hfaVu9LTVVzoXQlL7O85X+3TxPSzNedzet9tMd09Ld/q278nDMwzwcY58WUZIk8o355BnyKDQVIiGhkCkY8MVBrmXLHPLjHjip4TMXv18lPKNSsN9HKK90eaNaj2LW77MYtWEUB1846DSIk7O2nMFV+ICS4sT1E4xYNYID6QcY2mQoc3rPIdgnGLAIoYOXbrJw/2XMkoRcEBjY0rUD0t/N87Sk43WXzxRKp9oRBAF/lb+DITMzO9mpM/L9qhb7q1Ap2O8jlJfu2E/lxxePfUHC4gSm7prK+13fL3Wd8jJmJ9IZdUzfPZ1pu6cRqA5k0cBFDGkyxK6MLUHHn2pFsySx/FAarWqFuhXu96sgdwZvx+vNra88k4iUJXRFJVyjUnl1H8ETt7wk6NewHyPiRvDBrx+QeDqx1HWWhOpYFJIkser0Kpp82YR3f3mXJxo/wcl/nXQQ6uDZC7YS3sObb+nMz6C0qixPdVk3mrJ6pv7dUCnY7yOU54ID+OKxL2gd3Zqhy4ey5cIWj205Q3QpNpXfLv9G5586k7A4AR+FD9ue2cYTtT+m/6zjTh1s/m4slzsJb76lp3ATJUFZQ1dUwjkqVTH3EbzVpXp7tdUoNaz7xzq6zevG4wsf59s+39pC3xZvyxUrxttNRZIkfrn0C9N2T2PThU1E+EUw57E5vNDyBdYmX3OrHrgX8oveK7gb39Kdmqhy0y4dKgX7fQZPutSSMmfCfMPY8ewOBi4ZyDOJz7D14la6RY3n6x3XHYxrpdGF5hvyWXpyKbN/n82hjEOE+4Yzvdt0RrUehZ/KD/BsFP67sVzuJLz5ln+l566rjUYmCCQmpVXq2l2grKnx3gP6ASJwHRguSVK6p/cqeex3D6XlcBvNRt7d9S4f7p4GooYAUz8CTI8hJ6jEfHWdUcf2i9tZenIpK06tINeQS6PwRoxuPZpnmj/jECfbkxckVBrYyhOevuVf6QfgjE9vxZ3yk6jI+Kt47DMkSXrnzwbHAP8BPOY8rcTdQ2mvtkq5kve6vsfafbU5o/+abOUCshWL0Ijx+Jhb8p8Nf9Ct0dMEqAPs3jOYDVzOvszJzJMczjjM7su72Z26G71JT6A6kEGNBjEibgQdanZwGcLAG/XA343lcifh6Vv+leoRdzGHyttP4n5CmQS7JEk5Rf7ph2MEzkpUMJRVh6rNiaAq/8Hw/+3de4xcZRnH8e+P7fZOAakW3HYoxKZK2pKqIVUShRTNoqRtAhqMl8aaFBNEIBil9A/+MmniPdGYGERJaFBSMRCvtGDiHwYiAipYFYLSLq62RuW2JO3Wxz/OqdksszuX8+68c6a/T7LpzJnZOc+bzjx75jnv+xwd4pWhA0wM/YpX5z/Kv4/Dsj3XsWR4CacvOJ3TdBoTxyf+f91KACHWr1jPtW+7ltE3jXLZ6stYMO+1bQCmc6mlv/S6Dr9t4wg3ff+Jpo+51t5c5Rq7pM8DHwNeAGZsLiJpJ7AToNFoVN2tdalqkjz5oZ4fDeZP7uCsyR1M6ghLlx5mx6ULGX9pnJePvUwQLB5ezNmLzqZxRoO1y9eyYcWGrjrtnWoLivpdjj+0PkHemZY1dkkHgHOaPLQ7Iu6b8rxdwMKIuK3VTl1jz6tKPXq2HiJOtKeOXp/T8Puu0G6NPVkTMEnnAT+OiHWtnuvEXm/NPtTgI2qbWz5B3qPELmlNRDxd3r4eeHdEXN3q95zYB4uPpsx6o1ezYvZIWksx3fE5PCPmlDTTPPOb7ykusefkbtZbVWfFXJUqEKuvmWYmnIjoaOGKv2qbpeFeMVbZbDMT2u3r4WZPZuk4sVtlrRqCtTPX2M2ezNJxrxirbLbVgdDeXOPZVjO6RGPWGR+xWxLbNo7wpQ9e1HXb4JmS/xmLhl2iMeuQE7slU6VPd7NyjiiupeoSjVlnXIqxpLppxnWy1PLq8RMMSZyIQMzeeGim0o3LNmZO7JbZ9MVN7SR1aF666WWfcLN+5lKMZdVsNkyrpD5T3d4za8wKPmK3rDptuzoyS3nFl1EzKzixW1YztWOdXo5pp/eMW7uaFVyKsayazYZZNDzEhzc1Op5dM9Nr+YIcdqrxEbtllfIiGr4gh1khWT/2Trhtr5lZ59pt2+tSjJnZgHFiNzMbME7sZmYDJklil/QZSSFpeYrXMzOz7lVO7JJWAe8BDlUPx8zMqkpxxP4V4LO0XgluZmY9UCmxS9oCPB8Rv00Uj5mZVdRygZKkA8A5TR7aDdwKvLedHUnaCewEaDQaHYRoZmad6HqBkqT1wIPARLlpJfA34OKI+HuL3z0KPDdl03Lgn10F0p8GbTzgMdWFx1QP3Y7pvIh4fasnJVt5KumvwNsjouNgJT3azmqquhi08YDHVBceUz3M9Zg8j93MbMAkawIWEatTvZaZmXWvX47Yv5U7gMQGbTzgMdWFx1QPczqmLN0dzcxs7vTLEbuZmSXSF4ld0hck/VHS7yT9UNKZuWPqlqRRSX+S9IykW3LHU5WkVZJ+IemgpKck3ZA7phQkDUl6XNKPcseSgqQzJe0rP0cHJb0jd0xVSbqpfM89KeluSQtzx9QpSXdIOiLpySnbXidpv6Sny3/PSr3fvkjswH5gXURsAP4M7MocT1ckDQHfAK4ALgQ+JOnCvFFVNgncHBFvATYB1w3AmABuAA7mDiKhrwE/i4g3AxdR87FJGgE+TTGFeh0wBFyTN6qufBcYnbbtFuDBiFhDsRYo+QFgXyT2iHggIibLuw9TLHaqo4uBZyLi2Yg4BnwP2Jo5pkoiYjwiHitvv0SRMGp9rTlJK4H3A7fnjiUFScuAdwHfBoiIYxHxn7xRJTEPWCRpHrCYYgFkrUTEL4F/Tdu8FbizvH0nsC31fvsisU+zA/hp7iC6NAIcnnJ/jJonwakkrQY2Ao/kjaSyr1I0rvtv7kASuQA4CnynLC/dLmlJ7qCqiIjngS9SdI0dB16IiAfyRpXMiogYh+LACXhD6h30LLFLOlDWyqb/bJ3ynN0UX/339iquxNRk20BMO5K0FPgBcGNEvJg7nm5JuhI4EhG/yR1LQvOAtwLfjIiNwCvMwdf7XirrzluB84E3AkskfSRvVPWRbIFSKxFx+WyPS9oOXAlsjvrOwRwDVk25f7J/Tq1JGqZI6nsj4t7c8VR0CbBF0vuAhcAySXdFRJ2TxhgwFhEnv0nto+aJHbgc+EtEHAWQdC/wTuCurFGl8Q9J50bEuKRzgSOpd9AXpRhJo8DngC0RMdHq+X3s18AaSedLmk9xsuf+zDFVIkkUtduDEfHl3PFUFRG7ImJluVL6GuChmid1yqZ7hyWtLTdtBv6QMaQUDgGbJC0u34ObqfkJ4SnuB7aXt7cD96XeQc+O2Fv4OrAA2F/8H/JwRHwyb0idi4hJSZ8Cfk5xFv+OiHgqc1hVXQJ8FPi9pCfKbbdGxE8yxmSvdT2wtzygeBb4eOZ4KomIRyTtAx6jKM8+Tg1XoEq6G7gUWC5pDLgN2APcI+kTFH/APpB8v/WtepiZWTN9UYoxM7N0nNjNzAaME7uZ2YBxYjczGzBO7GZmA8aJ3cxswDixm5kNGCd2M7MB8z9lsDae96CpxgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#查看概率分布：可以看到效果与我们人工生成的差不多\n",
    "utils.plot_contourf(X,gmm.predict_sample_generate_proba,lines=5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#查看分类边界\n",
    "utils.plot_decision_function(X,gmm.predict(X),gmm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "显然利用EM进行的无监督训练的GMM可以用于聚类任务，另外GMM用于分类也是可以的，思路同上面第二点一样，只是无需用到EM算法，下一节简单实现一下并作一定的扩展"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
